Equivalent material constant calculation system, storage medium storing an equivalent material constant calculation program, equivalent material constant calculation method, design system, and structure manufacturing method

ABSTRACT

An equivalent material constant calculation system that calculates an equivalent material constant of a structure constituted by a plurality of materials includes a shape data input portion that inputs shape data, a material data input portion that inputs material constant data, a dividing portion that divides the structure into a plurality of small regions, and a small region interior calculation portion that calculates equivalent material constants in the small regions, in which the small region interior calculation portion, based on the shape data and material constant data, with a function that includes a value in a variable that expresses a position in at least one direction in the small region, expresses an equivalent material constant for a region that is a portion of a small region, and using the function, calculates an equivalent material constant for the small region with respect to the at least one direction.

CROSS-REFERENCE TO RELATED MATTERS

This application is a Division of application Ser. No. 11/259,835, filedOct. 27, 2005, which application is incorporated herein by reference.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to an equivalent material constantcalculation system that calculates an equivalent material constant of astructure made from a plurality of materials having different materialconstants, an equivalent material constant calculation program, anequivalent material constant calculation method, and a design system andmanufacturing method for such a structure.

2. Description of Related Art

For example, in the design of electronic equipment, it is possible tomodel the electronic equipment such that the electronic equipment can behandled as data on a computer, and predict temperature, stress, and thelike by performing a simulation that employs, for example, a finiteelement method.

When modeling electronic equipment, the shape of components thatconstitute the electronic equipment, the material constant, and the likeare necessary as data. For example, the shape of an electronic circuitboard that is a component part of the electronic equipment and thematerial constant (for example, thermal conductivity) are necessary asdata. The electronic circuit board is configured of a wired portion madefrom metal material and a non-wired portion made from resin material.Thus, the electronic circuit board includes metal material and resinmaterial, which are materials with different material constants. In thiscase, it is not possible to model all of the wires using a computerhaving present day specifications. Consequently, it is necessary tosolve for an equivalent material constant by considering all or a partof the entire electronic circuit board, which is made from a pluralityof materials that have different material constants, as a structure madefrom a plurality of materials that have one equivalent materialconstant.

As a method of calculating this sort of equivalent material constant, acalculation method of an equivalent thermal conductivity that takes intoconsideration a wiring pattern on the electronic circuit board is known,as disclosed in JP 2000-180395A. FIG. 26 is a flowchart that shows anoverview of an electronic circuit board equivalent thermal conductivitycalculation method, and which is an example of this conventionalequivalent material constant calculation method.

In Step S911, shape data of the electronic circuit board that is thetarget of the equivalent thermal conductivity calculation is input. Theelectronic circuit board is configured by layering a wire pattern layer(hereinafter, referred to as a ‘wire layer’) and an insulation layer. Asshape data, for example, data relating to various shapes is input, suchas the outer contour of the entire electronic circuit board, theposition and size of holes in the electronic circuit board when suchholes exist, the thickness of the wire layer and the insulation layer,and the shape of the wire pattern in each wire layer.

In Step S912, material data of the electronic circuit board is input. Asmaterial data, for example, a thermal conductivity of the wire material,which is metal material that constitutes the wire pattern of theelectronic circuit board, and a thermal conductivity of the insulationmaterial, which is resin material that constitutes the insulation layerand the non-wire portion that is the portion other than the wirepattern, are input.

In Step S913, the electronic circuit board for which this equivalentthermal conductivity calculation will be performed is divided into anumber N of small regions of each wire layer and insulation layer ofthis electronic circuit board.

In Step S914, the wire pattern surface area and the insulating portionsurface area, which is the area other than the wire pattern, areobtained for each divided small region using the shape data of theelectronic circuit board that was input in above Step S911, and fromboth of these surface areas a surface area ratio of the wire portion ineach small region is calculated. Ordinarily the electronic circuit boardhas a very complicated shape, and reflecting this fact, the shape dataof this electronic circuit board also is very complicated. However, bydividing the electronic circuit board into small regions, the shape ofthe wire pattern in those small regions becomes, for example, a straightline or arc, or a square or triangle, or part of a circle, or a shapethat can be approximated by at least these shapes. As a result, it ispossible to calculate the wire pattern surface area and the other,insulation portion surface area with relative ease and high accuracy.

In Step S915, by adding up the wire portion surface area ratio of thesedivided N-small regions, a wire portion surface area ratio is calculatedfor each wire layer or insulation layer. The formula for obtaining thewire portion surface area ratio for each of these layers is shown informula 1. Pi in formula 1 indicates the wire portion surface area ratioof a layer No. i.

$\begin{matrix}{P_{i} = {\sum\limits_{j = 1}^{N}{p_{ij}/N}}} & {{Formula}\mspace{14mu} 1}\end{matrix}$In formula 1, P_(ij) is the wire portion surface area ratio of a smallregion No. j of the layer No. i.

This formula obtains an average of the wire portion surface area ratiosof each small region. However, here it is assumed that the surface areaof the divided small regions is equal.

In Step S916, an equivalent thermal conductivity λp of the entireelectronic circuit board that is regarded as lamination material iscalculated using the wire portion surface area ratio calculated for eachof the wire and insulation layers.

It is possible to use formula 2 or formula 3 for this calculation of λp.Formula 2 is a formula for a case in which the thermal conductivityeffect of the insulator material is ignored. Ordinarily, the thermalconductivity of the insulator material is very small in comparison tothe thermal conductivity of the wire material, and so it is possible tolighten the calculation load by ignoring the thermal conductivity effectof the insulator material as in formula 2. Formula 3 is a formula for acase in which the thermal conductivity effect of the insulator materialis taken into consideration.

$\begin{matrix}{\mspace{79mu}{\lambda_{p} = {\sum\limits_{i}\left( {\lambda_{i}P_{i}\alpha_{i}} \right)}}} & {{Formula}\mspace{14mu} 2} \\{\mspace{79mu}{{\lambda_{p} = {A + B}}{A = {\sum{\left( {\left( {{\lambda_{A}P_{i}} + {\lambda_{B}\left( {1 - P_{i}} \right)}} \right)\alpha_{i}} \right)\mspace{14mu}\left( {\sum\mspace{14mu}{{is}\mspace{14mu}{wire}\mspace{14mu}{layer}\mspace{14mu}{sum}\mspace{14mu}{only}}} \right)}}}\mspace{79mu}{B = {\sum{\left( {\lambda_{B}\alpha_{i}} \right)\mspace{14mu}\left( {\sum\mspace{14mu}{{is}\mspace{14mu}{insulation}\mspace{14mu}{layer}\mspace{14mu}{sum}\mspace{14mu}{only}}} \right)}}}}} & {{Formula}\mspace{14mu} 3}\end{matrix}$In Formula 2, λ_(i), P_(i), and α_(i) indicate the following values:

-   λ_(i): thermal conductivity of the wire material of layer No. i    (W/m·K)-   P_(i): wire portion surface area ratio of layer No. i (0.0 for the    insulation layer)-   α_(i): ratio at which the thickness of layer No. i accounts for the    thickness of the entire electronic circuit board (see Formula 4).

$\begin{matrix}{{\sum\limits_{i}\alpha_{i}} = 1} & {{Formula}\mspace{14mu} 4}\end{matrix}$In formula 3, λ_(A) and λ_(B) indicate the following values. P_(i) andα_(i) are the same as in formula 2.

-   λ_(A): thermal conductivity of the wire material (W/m·K)-   λ_(B): thermal conductivity of the insulator material (W/m·K)

In formula 3, portions of the wire material that are included in theinsulation layer (such as through holes) are ignored. If portions of thewire material that are included in the insulation layer also areconsidered, then it is possible to perform the calculation for B informula 3 in the same manner as the calculation for A.

Further, in formula 3, it is assumed that the wire material of eachlayer and also the insulator material of each layer are the same (or atleast that the thermal conductivity of the wire material of each layeris the same, and that the thermal conductivity of the insulator materialof each layer is the same).

In Step S917, equivalent thermal conductivity information for the entireelectronic circuit board that was calculated in Step S916 is output to athermal conductivity database or the like. The equivalent thermalconductivity saved in the thermal conductivity database afterwards canbe read and used when performing a thermal conductivity analysis thatemploys a finite element method or the like.

However, in the conventional equivalent material constant calculationmethod described above, an equivalent material constant is calculatedusing a surface area ratio of the occupied surface area of eachelectronic material (wire material and insulator material), but thedirectionality of the shape of the portion occupied by each electronicmaterial on the electronic circuit board is not considered at all.

Even assuming that a particular electronic material occupies the samesurface area on one board, the equivalent material constant differsgreatly according to the directionality of the shape of the portion onthat board that is occupied by that electronic material.

FIG. 27 shows an example of a wire pattern of an electronic circuitboard. For example, in an electronic circuit board 921 shown in FIG.27A, a wire pattern 923 constituted by wire material that is a goodthermal conductor occupies a long and narrow surface area along thedirection of the X axis, and six strips of that wire material arepresent. In this electronic circuit board 921, for example, when heat istransmitted in the direction of the X axis, the transmission of heat isgood because it is transmitted from one side to the opposite sidethrough the wire pattern 923, which is a good thermal conductor. On theother hand, when heat is transmitted in the direction of axis Y, thetransmission of heat becomes poor because it is transmitted alternatelythrough the wire pattern 923 and the non-wire portion 924. Accordingly,the equivalent thermal conductivity is comparatively high in thedirection of the X axis, and comparatively low in the directionperpendicular to direction X (the direction of the Y axis).

Conversely, as in an electronic circuit board 922 shown in FIG. 27B,when the wire pattern 923, which is constituted by wire material that isa good thermal conductor, occupies a long and narrow surface area alongthe direction of the Y axis and is present in seven strips, the thermalconductivity becomes comparatively high in the direction of the Y axis,and comparatively low in the direction of the X axis, which isperpendicular to the Y axis.

Because the equivalent material constant that can be obtained by theconventional equivalent material constant calculation method describedabove is calculated using a surface area ratio of the occupied surfacearea, the directionality of the shape of the portion occupied by eachelectronic material on the electronic circuit board is not taken intoconsideration at all. Thus, for example, as shown in FIGS. 27A and 27B,when the shape of the portion occupied by each material is anisotropic,the calculated equivalent material constant cannot avoid an extremelylarge error.

As one approach for solving this problem, for example, it has beenconceived to divide the electronic circuit board into even smallerregions and obtain an equivalent material constant for each of thedivided small regions, thereby reducing the size of the error. However,this approach makes a greater amount of calculation time necessary.Also, because the equivalent material constant for each small regiondoes not take into consideration the different directionality of theshape of the portion that each electronic material occupies, this methodhas little effectiveness for increasing the accuracy of an equivalentmaterial constant having anisotropy. Thus, there is the problem that theeffectiveness of calculation processing worsens.

Also, when the electronic circuit board is finely divided, the amount ofdata output as calculation results becomes large because as manyequivalent material constants are output as there are divided smallregions. Thus, analysis processing also becomes complicated whenanalysis is performed using the output equivalent material constants,and the effectiveness worsens.

SUMMARY OF THE INVENTION

Therefore, with the foregoing in mind, it is an object of the presentinvention to provide an equivalent material constant calculation systemin which it is possible to calculate with good effectiveness a highlyaccurate equivalent material constant that takes into consideration thedirectionality of each material in a structure constituted by aplurality of materials, an equivalent material constant calculationprogram, an equivalent material constant calculation method, and also adesign system and manufacturing method for that sort of structure.

An equivalent material constant calculation system according to thepresent invention calculates an equivalent material constant of astructure constituted by a plurality of materials, and includes a shapedata input portion that inputs shape data that expresses the shape ofeach material constituting the structure, a material data input portionthat inputs material constant data that expresses a material constant ofat least one of the materials constituting the structure, a dividingportion that divides the structure into a plurality of small regions,and a small region interior calculation portion that calculatesequivalent material constants in the small regions, wherein the smallregion interior calculation portion, based on the shape data andmaterial constant data, expresses an equivalent material constant for aregion that is part of a small region, with a function that includes avalue in a variable that expresses a location in at least one directionin the small regions, and using the function, calculates equivalentmaterial constants in the small region with respect to the at least onedirection.

An equivalent material constant calculation system according to thepresent invention calculates an equivalent material constant of astructure constituted by a plurality of materials, and includes a shapedata input portion that inputs shape data that expresses the shape ofeach material constituting the structure, a material data input portionthat inputs material constant data that expresses a material constant ofat least one of the materials constituting the structure, a dividingportion that divides the structure into a plurality of small regions,and a small region interior calculation portion that calculatesconstituent ratios of the materials included in the small regions basedon the shape data, and calculates equivalent material constants in thesmall regions based on the constituent ratios and the material constantdata, and a combining portion that, based on the equivalent materialconstants for the small region, obtains an equivalent material constantfor a region in which a plurality of the small regions that are adjacentare combined.

An equivalent material constant calculation program stored on a storagemedium according to the present invention allows a computer to executeprocessing that calculates an equivalent material constant of astructure constituted by a plurality of materials, the processingincluding shape data input processing that inputs shape data thatexpresses the shape of each material constituting the structure,material data input processing that inputs material constant data thatexpresses a material constant of at least one of the materialsconstituting the structure, dividing processing that divides thestructure into a plurality of small regions, and small region interiorcalculation processing that calculates equivalent material constants inthe small regions. The small region interior calculation processing,based on the shape data and material constant data, expresses anequivalent material constant for a region that is a portion of a smallregion, with a function that includes a value in a variable thatexpresses a position in at least one direction in the small regions, andusing the function, calculates an equivalent material constant for thesmall region with respect to the at least one direction.

An equivalent material constant calculation program stored on a storagemedium according to the present invention allows a computer to executeprocessing that calculates an equivalent material constant of astructure constituted by a plurality of materials. The processingincludes shape data input processing that inputs shape data thatexpresses the shape of each material constituting the structure,material data input processing that inputs material constant data thatexpresses a material constant of at least one of the materialsconstituting the structure, dividing processing that divides thestructure into a plurality of small regions, small region interiorcalculation processing that calculates constituent ratios of thematerials included in the small region based on the shape data, andcalculates an equivalent material constant for the small region based onthe constituent ratio and the material constant data, and combiningprocessing that, based on the equivalent material constant for the smallregion, obtains an equivalent material constant for a region in which aplurality of the small regions that are adjacent are combined.

An equivalent material constant calculation method according to thepresent invention calculates an equivalent material constant of astructure constituted by a plurality of materials using a computer. Themethod includes a shape data input step in which a shape data inputportion provided by the computer inputs shape data that expresses theshape of each material constituting the structure, a material data inputstep in which a material data input portion provided by the computerinputs material constant data that expresses a material constant of atleast one of the materials constituting the structure, a dividing stepin which a dividing portion provided by the computer divides thestructure into a plurality of small regions, and a small region interiorcalculation step in which a small region interior calculation portionprovided by the computer calculates equivalent material constants in thesmall regions, in which in the small region interior calculation step, asmall region interior calculation portion, based on the shape data andmaterial constant data, expresses an equivalent material constant for aregion that is a portion of a small region, with a function thatincludes a value in a variable that expresses a location in the smallregion in at least one direction, and using the function, calculates anequivalent material constant for the small region with respect to the atleast one direction

An equivalent material constant calculation method according to thepresent invention calculates an equivalent material constant of astructure constituted by a plurality of materials using a computer. Themethod includes a shape data input step in which a shape data inputportion provided by the computer inputs shape data that expresses theshape of each material constituting the structure, a material data inputstep in which a material data input portion provided by the computerinputs material constant data that expresses a material constant of atleast one of the materials constituting the structure, a dividing stepin which a dividing portion provided by the computer divides thestructure into a plurality of small regions, a small region interiorcalculation step in which a small region interior calculation portionprovided by the computer calculates a constituent ratio of the materialsincluded in the small region based on the shape data, and calculates anequivalent material constant for the small region based on theconstituent ratio and the material constant data, and a combining stepin which a combining portion provided by the computer, obtains anequivalent material constant for a region in which a plurality of thesmall regions that are adjacent are combined, based on the equivalentmaterial constant for the small region.

Due to the present invention adopting the configuration described above,in a structure constituted by a plurality of materials, it is possibleto calculate efficiently a highly accurate equivalent material constantthat takes into consideration the directionality of each material.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A is a functional block diagram that shows the configuration of anequivalent material constant calculation system. FIG. 1B is a functionalblock diagram that shows an example of the configuration of anequivalent material constant calculation system in which the function ofthe equivalent material constant calculation system 1 is distributed toa terminal system 1 a and server system 1 b.

FIG. 2 is a functional block diagram that shows the configuration of asmall region interior calculation portion 6.

FIG. 3 is a flowchart that shows the operation of an equivalent materialconstant calculation system 1.

FIG. 4 shows an example of the shape of a wire layer included in anelectronic circuit board for which an equivalent thermal conductivitycalculation is performed.

FIG. 5 is a flowchart that shows the detailed flow of processing thatcalculates an equivalent thermal conductivity for each small region 102.

FIG. 6 shows an example of a selected small region 102.

FIG. 7A shows a condition in which heat is transmitted parallel to thedirection of the X axis in a section K1 of a small region 102. FIG. 7Bshows a condition in which heat flows parallel to the direction of awire pattern portion 303.

FIG. 8 shows a heat path length and a heat path width of a wire.

FIG. 9 is a functional block diagram that shows the configuration of asmall region interior calculation portion 6.

FIG. 10 is a flowchart that shows the detailed flow of processing thatcalculates an equivalent thermal conductivity for each small region 102.

FIG. 11 shows an example of a selected small region 102.

FIG. 12 is a flowchart that shows the detailed flow of processing thatcalculates an equivalent thermal conductivity for a small region 102.

FIG. 13A shows an example of a selected small region 102. FIG. 13B showsan example of equivalent material constants calculated respectivelyusing an arithmetic mean, weighted mean, maximum value, and minimumvalue as θav.

FIG. 14 is a functional block diagram that shows an example of theconfiguration of an equivalent material constant calculation system 10.

FIG. 15 is a flowchart that shows the operation of an equivalentmaterial constant calculation system.

FIG. 16 shows one selected small region 102.

FIG. 17 is a cross-sectional diagram viewing one of the small regions102 in the XZ plane.

FIG. 18 is a plan view viewing four adjacent small regions 601, 602,603, and 604 in the XY plane.

FIG. 19 is a plan view viewing three adjacent small regions 701, 702,and 703 from the direction of the Z axis.

FIG. 20 is a functional block diagram that shows the configuration of anequivalent material constant calculation system.

FIG. 21 is a flowchart that shows the operation of an equivalentmaterial constant calculation system 100.

FIG. 22 shows an example in which small regions 102 are more finelydivided.

FIG. 23 shows an example of a medium region included in an electroniccircuit board 101.

FIG. 24 is a functional block diagram that shows an example of theconfiguration of a design system 15.

FIG. 25 is a flowchart that shows the flow of processing in which adesign system 15 manufactures a structure.

FIG. 26 shows an example of a conventional equivalent material constantcalculation method.

FIGS. 27A and 27B show examples of a wire pattern of an electroniccircuit board.

DETAILED DESCRIPTION OF THE INVENTION

An equivalent material constant calculation system according to thepresent invention calculates an equivalent material constant of astructure constituted by a plurality of materials, and includes a shapedata input portion that inputs shape data that expresses the shape ofeach material constituting the structure, a material data input portionthat inputs material constant data that expresses a material constant ofat least one of the materials constituting the structure, a dividingportion that divides the structure into a plurality of small regions,and a small region interior calculation portion that calculatesequivalent material constants in the small regions. The small regioninterior calculation portion, expresses based on the shape data andmaterial constant data, an equivalent material constant for a regionthat is part of a small region, with a function that includes a value ina variable that expresses a position in at least one direction in thesmall regions, and calculates equivalent material constants in the smallregion with respect to the at least one direction using the function.

The small region interior calculation portion, based on the shape dataand material constant data, with a function that includes a value thatexpresses a location in at least one direction in the small regions in avariable, expresses an equivalent material constant for a region that ispart of a small region. Because the small region interior calculationportion calculates equivalent material constants in a small region usingthe function, it is possible to calculate an equivalent materialconstant with respect to at least one direction.

In the equivalent material constant calculation system according to thepresent invention, it is preferable that the small region interiorcalculation portion includes a boundary function generating portion thatsets a coordinate in the direction of one coordinate axis to u in anorthogonal coordinate system that has been set for the structure, andgenerates, based on the shape data, a boundary function F(u) thatexpresses a boundary between the materials in a small region, a sectionsetting portion that sets one or two or more sections for u in the smallregion according to a domain of the boundary function F(u), a sectioninterior calculation portion that creates, in the section, based on thefunction F(u) and the material constant data, a function that expressesa position where the material constant is applied, and obtains anequivalent material constant of the coordinate axis direction in thesection by integrating the function in the section, and an equivalentmaterial constant generating portion that, based on a section equivalentmaterial constant of each section obtained by the section interiorcalculation portion, obtains an equivalent material constant of thecoordinate axis direction in the small region.

Because the small region interior calculation portion obtains anequivalent material constants for the direction of one coordinate in thesmall region using the boundary function F(u), it is possible to obtainefficiently an equivalent material constant that takes intoconsideration the directionality of each material in the small region.

In the equivalent material constant calculation system according to thepresent invention, it is preferable that the small region interiorcalculation portion includes a minimum region material constantgenerating portion that further divides the small regions into aplurality of minimum regions along one or two or more directions, andobtains an equivalent material constant for each minimum region based onthe shape data and the material constant data, a spectrum calculationportion that obtains a frequency spectrum in each minimum region byperforming a Fourier transformation of the distribution of theequivalent material constant of the minimum regions in the small regionin one or two or more directions, and an equivalent material constantgenerating portion that obtains an equivalent material constant for thesmall region in the one or two or more directions, based on thefrequency spectrum in each of the minimum regions.

Because the small region interior calculation portion obtains anequivalent material constant of the small region based on a frequencyspectrum for each minimum region obtained by performing a Fouriertransformation of the distribution of the equivalent material constantof the minimum regions in the small region from the minimum regionmaterial constant generating portion in one or two or more directions,it is possible to obtain efficiently an equivalent material constantthat takes into consideration the directionality of each material in thesmall region.

It is preferable that the equivalent material constant calculationsystem according to the present invention includes a combining portionthat obtains, based on the equivalent material constant for the smallregion, an equivalent material constant for a region in which aplurality of small regions that are adjacent are combined.

Because the combining portion obtains an equivalent material constantfor a region in which a plurality of small regions that are adjacent arecombined based on the equivalent material constant for the small region,it is possible to reduce the data quantity of the equivalent materialconstants obtained as calculation results as necessary.

It is preferable that in the equivalent material constant calculationsystem according to the present invention, the combining portion obtainsthe equivalent material constant for a region in which a plurality ofthe small regions that are adjacent are combined, by deeming theequivalent material constant for each of the plurality of small regionsto be a mutually connected resistance, and obtaining a combinedresistance.

An equivalent material constant calculation system according to thepresent invention calculates an equivalent material constant of astructure constituted by a plurality of materials, and includes a shapedata input portion that inputs shape data that expresses the shape ofeach material constituting the structure, a material data input portionthat inputs material constant data that expresses a material constant ofat least one of the materials constituting the structure, a dividingportion that divides the structure into a plurality of small regions,and a small region interior calculation portion that calculatesconstituent ratios of the materials included in the small regions basedon the shape data, and calculates equivalent material constants in thesmall regions based on the constituent ratios and the material constantdata, and a combining portion that obtains, based on the equivalentmaterial constants for the small region, an equivalent material constantfor a region in which a plurality of the small regions that are adjacentare combined.

With the equivalent material constant calculation system according tothe present invention, even when the dividing portion has finely divideda structure into a large number of small regions, and the small regioninterior calculation portion has obtained equivalent material constantsfor a large number of finely divided small regions, an equivalentmaterial constant is obtained by the combining portion for a region inwhich a plurality of the small regions that are adjacent are combined.Thus, it is possible to reduce the data quantity of the equivalentmaterial constants obtained as calculation results as necessary.

It is preferable that in the equivalent material constant calculationsystem according to the present invention, the dividing portion dividesthe structure into a plurality of layers, and divides the divided layersinto small regions, and the combining portion includes a laminationdirection combining portion that obtains an equivalent material constantof a region in which the small regions of the layers are combined in thelamination direction, based on an equivalent material constant of thesmall regions of each layer, and a perpendicular direction combiningportion that obtains an equivalent material constant of a region inwhich the small regions that are adjacent are combined in the directionperpendicular to the lamination direction.

Because the combining portion obtains an equivalent material constant ofa region in which the small regions divided into each layer by thedividing portion are combined in the lamination direction, and anequivalent material constant of a region in which adjacent small regionsthat are adjacent are combined in the direction perpendicular to thelamination direction, an equivalent material constant of the combinedregion can be obtained efficiently.

It is preferable that in the equivalent material constant calculationsystem according to the present invention, the combining portion deemsthe equivalent material constant for each of the combined plurality ofsmall regions to be a mutually connected resistance, and usingKirchoff's law, obtains an equivalent material constant for a region inwhich a plurality of the small regions that are adjacent are combined.

By using Kirchoff's law, the combining portion can obtain efficiently anequivalent material constant for a region in which a plurality of thesmall regions that are adjacent are combined.

In the equivalent material constant calculation system according to thepresent invention, it is possible to adopt a configuration wherein thestructure is an electronic circuit board, and the material constant isthermal conductivity or thermal resistance.

In the equivalent material constant calculation system according to thepresent invention, it is possible to adopt a configuration wherein thestructure is an electronic circuit board, the material constant isthermal conductivity or thermal resistance, and the layer is a wirelayer or an insulation layer of the electronic circuit board.

A storage medium storing an equivalent material constant calculationprogram according to the present invention allows a computer to executeprocessing that calculates an equivalent material constant of astructure constituted by a plurality of materials. The processingincludes shape data input processing that inputs shape data thatexpresses the shape of each material constituting the structure,material data input processing that inputs material constant data thatexpresses a material constant of at least one of the materialsconstituting the structure, dividing processing that divides thestructure into a plurality of small regions, and small region interiorcalculation processing that calculates equivalent material constants inthe small regions, in which the small region interior calculationprocessing, based on the shape data and material constant data,expresses an equivalent material constant for a region that is a portionof a small region, with a function that includes a value in a variablethat expresses a position in at least one direction in the smallregions, and calculates an equivalent material constant for the smallregion with respect to the at least one direction using the function.

In the equivalent material constant calculation program according to thepresent invention, it is preferable that the small region interiorcalculation processing includes boundary function generating processingthat sets a coordinate in the direction of one coordinate axis to u inan orthogonal coordinate system that has been set for the structure, andgenerates, based on the shape data, a boundary function F(u) thatexpresses a boundary between the materials in a small region, sectionsetting processing that sets one or two or more sections for u in thesmall region according to a domain of the boundary function F(u),section interior calculation processing that creates, in the section,based on the function F(u) and the material constant data, a functionthat expresses a position where the material constant is applied, andobtains an equivalent material constant of the coordinate axis directionin the section by integrating the function in the section, andequivalent material constant generating processing that, based on asection equivalent material constant of each section obtained by thesection interior calculation portion, obtains an equivalent materialconstant of the coordinate axis direction in the small region.

In the equivalent material constant calculation program according to thepresent invention, it is preferable that the small region interiorcalculation processing includes minimum region material constantgenerating processing that further divides each of the small regionsinto a plurality of minimum regions along one or two or more directions,and obtains an equivalent material constant for each minimum regionbased on the shape data and the material constant data, spectrumcalculation processing that obtains a frequency spectrum in each minimumregion by performing a Fourier transformation of the distribution of theequivalent material constant of the minimum regions in the small regionin one or two or more directions, and equivalent material constantgenerating processing that obtains an equivalent material constant forthe small region in the one or two or more directions, based on thefrequency spectrum in each of the minimum regions.

An equivalent material constant calculation program stored on a storagemedium according to the present invention allows a computer to executeprocessing that calculates an equivalent material constant of astructure constituted by a plurality of materials. The processingincludes shape data input processing that inputs shape data thatexpresses the shape of each material constituting the structure,material data input processing that inputs material constant data thatexpresses a material constant of at least one of the materialsconstituting the structure, dividing processing that divides thestructure into a plurality of small regions, small region interiorcalculation processing that calculates constituent ratios of thematerials included in the small region based on the shape data, andcalculates an equivalent material constant for the small region based onthe constituent ratio and the material constant data, and combiningprocessing that, obtains, based on the equivalent material constant forthe small region, an equivalent material constant for a region in whicha plurality of the small regions that are adjacent are combined.

An equivalent material constant calculation method according to thepresent calculates an equivalent material constant of a structureconstituted by a plurality of materials using a computer. The methodinclude a shape data input step in which a shape data input portionprovided by the computer inputs shape data that expresses the shape ofeach material constituting the structure, a material data input step inwhich a material data input portion provided by the computer inputsmaterial constant data that expresses a material constant of at leastone of the materials constituting the structure, a dividing step inwhich a dividing portion provided by the computer divides the structureinto a plurality of small regions, and a small region interiorcalculation step that calculates equivalent material constants in thesmall regions, wherein the small region interior calculation step, inwhich a small region interior calculation portion provided by thecomputer expresses, based on the shape data and material constant data,an equivalent material constant for a region that is a portion of asmall region, with a function that includes a value in a variable thatexpresses a location in the small region in at least one direction, andcalculates an equivalent material constant for the small region withrespect to the at least one direction using the function.

In the equivalent material constant calculation method according to thepresent invention, it is preferable that the small region interiorcalculation step includes a boundary function generating step of settinga coordinate in the direction of one coordinate axis to u in anorthogonal coordinate system that has been set for the structure, andgenerating, based on the shape data a boundary function F(u) thatexpresses a boundary between the materials within the small region, asection setting step of setting one or more sections for u in the smallregion according to a domain of the boundary function F(u), a sectioninterior calculation step of creating, in the section a function thatexpresses a position where the material constant is applied, based onthe function F(u) and the material constant data, and obtaining anequivalent material constant of the coordinate axis direction in thesection by integrating the function in the section, and an equivalentmaterial constant generating step of obtaining an equivalent materialconstant of the coordinate axis direction in the small region, based ona section equivalent material constant of each section which is obtainedin the section interior calculation step.

In the equivalent material constant calculation method according to thepresent invention, it is preferable that the small region interiorcalculation step includes a minimum region material constant generatingstep of further dividing a small regions into a plurality of minimumregions along one or more directions, and obtaining an equivalentmaterial constant for each minimum region, based on the shape data andthe material constant data, a spectrum calculation step of obtaining afrequency spectrum in each minimum region by performing a Fouriertransformation of the distribution of the equivalent material constantof the minimum regions in the small region in one or more directions,and an equivalent material constant generating step of obtaining anequivalent material constant for the small region in the one or moredirections, based on the frequency spectrum in each of the minimumregions.

An equivalent material constant calculation method according to thepresent invention calculates an equivalent material constant of astructure constituted by a plurality of materials using a computer. Themethod includes a shape data input step in which a shape data inputportion provided by the computer inputs shape data that expresses theshape of each material constituting the structure, a material data inputstep in which a material data input portion provided by the computerinputs material constant data that expresses a material constant of atleast one of the materials constituting the structure, a dividing stepin which a dividing portion provided by the computer divides thestructure into a plurality of small regions, a small region interiorcalculation step in which a small region interior calculation portionprovided by the computer calculates a constituent ratio of the materialsincluded in the small region based on the shape data, and calculates anequivalent material constant for the small region based on theconstituent ratio and the material constant data, and a combining stepin which a combining portion provided by the computer obtains anequivalent material constant for a region in which a plurality of thesmall regions that are adjacent are combined, based on the equivalentmaterial constant for the small region.

An equivalent material constant calculation system according to thepresent invention that calculates an equivalent material constant of astructure constituted by a plurality of materials includes a shape datainput portion that inputs shape data that expresses the shape of eachmaterial constituting the structure, a material data input portion thatinputs material constant data that expresses a material constant of atleast one of the materials constituting the structure, a dividingportion that divides the structure into a plurality of small regions,and a small region interior calculation portion that calculatesequivalent material constants in the small regions, wherein the smallregion interior calculation portion calculates an area of each materialincluded in the small region based on the shape data, obtains a slope ofa line that expresses a boundary between the materials relative to apredetermined direction, and calculates an equivalent material constantfor the small region based on the slope, the area, and the materialconstant data.

Because the small region interior calculation portion calculates theequivalent material constant based on the slope, the area, and thematerial constant data, an equivalent material constant is calculatedthat takes into consideration the directionality of the shape of eachmaterial occupying part of the interior of the small region. Also, thesmall region interior calculating portion calculates the equivalentmaterial constant by obtaining the area and the slope. Thus, the smallregion interior calculating portion can calculate an equivalent materialconstant that takes into consideration the directionality with simplerprocessing than, for example, a method that divides the small regionsmore finely and analyzes that data.

An equivalent material constant calculation system according to thepresent invention calculates an equivalent material constant of astructure constituted by a plurality of materials, and includes a shapedata input portion that inputs shape data that expresses the shape ofeach material constituting the structure, a material data input portionthat inputs material constant data that expresses a material constant ofat least one of the materials constituting the structure, a dividingportion that divides the structure into a plurality of small regions, arepresentative material determining portion that determines a materialthat represents respective small regions for each of the plurality ofsmall regions, a material constant selection portion that selects thematerial constant of the material that represents the respective smallregions from the material constant data, and a combining portion thatcalculates an equivalent material constant for a region in which aplurality of the small regions that are adjacent are combined withrespect to at least one direction, by combining the material constant ofthe representative material of the plurality of adjacent small regionsin at least one direction.

With the equivalent material constant calculation system according tothe present invention, the representative material determining portiondetermines a representative material for each small region divided bythe dividing portion, and the material constant of that representativematerial is selected by the material constant selection portion. Becauseit is not necessary to calculate the material constants of the smallregions, no time is required to determine the material constants of thesmall regions. The combining portion, by combining the materialconstants given one at a time to each small region with respect to atleast one direction, can obtain an equivalent material constant thattakes into consideration directionality with a simple calculation. As aresult, it is possible to calculate efficiently an equivalent materialconstant that takes into consideration anisotropy of the structure.

Also, even when the dividing portion has finely divided the structureinto a large number of small regions, an equivalent material constant isobtained by the combining portion for a region in which a plurality ofadjacent small regions are combined. Thus, it is possible to decreasethe data quantity of equivalent material constants obtained ascalculation results as necessary.

It is preferable that in the equivalent material constant calculationsystem according to the present invention, the dividing portion dividespart of the structure into a plurality of small regions, and therepresentative material determining portion, the material constantselection portion, and the combining portion perform processing for theregions of part of the structure divided by the dividing portion.

In this way, because the processing that calculates an equivalentmaterial constant for a region that is a part of the structure dividedby the dividing portion is performed, it is possible to omit processingthat calculates an equivalent material constant of locations unnecessaryfor analysis. Thus, it is possible to achieve a shortening ofcalculation time.

It is preferable that in the equivalent material constant calculationsystem according to the present invention, the combining portioncalculates an equivalent material constant for each medium region inwhich a plurality of adjacent small regions are combined, and the mediumregion is a region that is part of the structure, and a plurality of themedium regions are included in the structure.

By doing so, an equivalent material constant is calculated for eachmedium region that constitutes a part of the structure. Thus, it ispossible to express compression of the material that constitutes thestructure with the size of the equivalent material constant. That is,because an equivalent material constant is obtained for a plurality ofmedium regions included in the structure, a distribution of theequivalent material constants in the structure is obtained.

It is preferable that in the equivalent material constant calculationsystem according to the present invention, the dividing portion dividesthe structure into small regions by dividing the structure into aplurality of layers parallel to each other, and further dividing eachlayer.

By doing so, for example, it is possible to divide a structure that hasa layer structure into a plurality of layers that are parallel to eachother according to the layer structure, and to further divide eachlayer. Due to the dividing portion dividing according to the layerstructure of the structure, the combining portion combines the dividedsmall regions and it is possible to obtain efficiently an equivalentmaterial constant.

It is preferable that in the equivalent material constant calculationsystem according to the present invention, the combining portion obtainsthe equivalent material constant by deeming the material constant of thematerial that represents the respective small regions in the pluralityof adjacent small regions to be a mutually connected resistance, andobtaining a combined resistance. For example, by deeming the materialconstant to be resistance when the material constant has characteristicssimilar to electrical resistance such as thermal resistance, it ispossible to obtain a combined resistance using a circuit equation. Thus,it is possible to obtain efficiently an equivalent material constant fora region in which a plurality of adjacent small regions are combined.

In the equivalent material constant calculation system according to thepresent invention, it is possible to adopt a configuration wherein thestructure is an electronic circuit board, and the material constant is athermal conductivity or thermal resistance.

In the equivalent material constant calculation system according to thepresent invention, it is possible to adopt a configuration wherein thestructure is an electronic circuit board, and the material constant is athermal conductivity or thermal resistance, and the layer is a wirelayer or an insulation layer of the electronic circuit board. By doingso, it is possible to calculate efficiently the equivalent thermalconductivity or the equivalent heat resistance of an electronic circuitboard that has a layer structure.

It is preferable that in the equivalent material constant calculationsystem according to the present invention, the structure is anelectronic circuit board, and the dividing portion divides the structureinto small regions whose maximum width is not greater than the minimumwidth of wire formed on the electronic circuit board. By doing so, it ispossible to calculate precisely the equivalent thermal conductivity ofan electronic circuit board that has a layer structure.

A design system according to the present invention includes theequivalent material constant calculation system according to the presentinvention, and includes a storage portion that stores design data of thestructure including the shape data and the material constant data, ananalysis portion that analyzes and outputs the flow of heat, stressdistribution electromagnetic fields, or hydrokinetics of the structure,by simulation based on the equivalent material constant of the structurecalculated by the equivalent material constant calculation system andthe design data, and a design modification portion that modifies thedesign data of the storage portion based on a command to modify thedesign data from a designer.

In the design system according to the present invention, the designportion performs analysis using the equivalent material constants of thestructure calculated by the equivalent material constant calculationsystem according to the present invention. The analysis portion canperform analysis using equivalent material constants that take intoconsideration directionality. Thus, in the analysis portion, analysis bysimulation that is closer to the actual phenomenon becomes possible.

Also, because an equivalent material constant of a region in which smallregions are combined is obtained by the equivalent material constantcalculation system, it is possible to put the characteristics of thestructure into the equivalent material constants without modeling theminimum regions of the structure. Thus, the number of elements (meshnumber) when performing analysis with the analysis portion decreases,and it is possible to shorten the analysis time greatly.

Because the amount of data of the equivalent material constantscalculated by the equivalent material constant calculation system islow, the amount of calculation in the analysis portion is also low. As aresult, efficient analysis is possible.

Also, the user can view the analysis results output by the analysisportion and submit a design data modification command to the designmodification portion. Thus, the analysis results are reflected in thedesign data, and high quality design data is obtained.

An equivalent material constant calculation method according to thepresent invention calculates an equivalent material constant of astructure constituted by a plurality of materials using a computer. Themethod includes a shape data input step in which a shape data inputportion provided by the computer inputs shape data that expresses theshape of each material constituting the structure, a material data inputstep in which a material data input portion provided by the computerinputs material constant data that expresses a material constant of atleast one of the materials constituting the structure, a dividing stepin which a dividing portion provided by the computer divides thestructure into a plurality of small regions, and a small region interiorcalculation step in which a small region interior calculation portionprovided by the computer calculates equivalent material constants in thesmall regions. In the small region interior calculation step, the smallregion interior calculation portion calculates an area of each materialincluded in the small region based on the shape data, obtains a slope ofa line that expresses a boundary between the materials relative to apredetermined direction, and calculates an equivalent material constantfor the small region based on the slope, the area, and the materialconstant data.

An equivalent material constant calculation method according to thepresent invention calculates an equivalent material constant of astructure constituted by a plurality of materials using a computer. Themethod includes a shape data input step in which a shape data inputportion provided by the computer inputs shape data that expresses theshape of each material constituting the structure, a material data inputstep in which a material data input portion provided by the computerinputs material constant data that expresses a material constant of atleast one of the materials constituting the structure, a dividing stepin which a dividing portion provided by the computer divides thestructure into a plurality of small regions, a representative materialdetermining step in which a representative material determining portionprovided by the computer determines a material that representsrespective small regions for each of the plurality of small regions, amaterial constant selection step in which a material constant selectionportion provided by the computer selects the material constant of thematerial that represents the respective small regions from the materialconstant data, and a combining step in which a combining portionprovided by the computer calculates an equivalent material constant fora region in which a plurality of the small regions that are adjacent arecombined with respect to at least one direction, by combining thematerial constant of the representative material of the plurality ofadjacent small regions in at least one direction.

A structure manufacturing method according to the present invention,using a computer that can access a storage device in which a pluralityof design data of a structure constituted by a plurality of materials isstored, manufactures the structure, and includes a calculating step inwhich the computer calculates an equivalent material constant of thestructure by the equivalent material constant calculation methodaccording to the present invention, an analysis step in which ananalysis portion provided by the computer analyzes the flow of heat,stress distribution, electromagnetic field, or hydrokinetics of thestructure, by simulation based on the equivalent material constant andthe design data, a design data selection step in which a design dataselection portion provided by the computer selects design data fromamong the plurality of design data based on the analysis resultsobtained by the analysis step for a structure expressed by the pluralityof design data stored in the storage device, and a manufacturing step inwhich a CAM, connected such that data communications are possible withthe computer, manufactures a structure based on the design data selectedby the design data selection step.

In the combining step of the manufacturing method according to thepresent invention, by combining a material constant of the selectedrepresentative material with respect to at least one direction, anequivalent material constant of the structure can be calculatedefficiently for each small region divided by the dividing step thattakes into consideration directionality. In the analysis step, becausethe analysis portion performs analysis using an equivalent materialconstant that takes into consideration directionality, analysis bysimulation that is close to the actual phenomenon becomes possible.Optimum design data is selected based on these analysis results. CAMmanufactures the structure based on the optimum design data. As aresult, a structure having the optimum structure is effectivelymanufactured.

A storage medium storing an equivalent material constant calculationprogram according to the present invention allows a computer to executeprocessing that calculates an equivalent material constant of astructure constituted by a plurality of materials. The processingincludes a shape data input processing that inputs shape data thatexpresses the shape of each material constituting the structure, amaterial data input processing that inputs material constant data thatexpresses a material constant of at least one of the materialsconstituting the structure, a dividing processing that divides thestructure into a plurality of small regions, and a small region interiorcalculation processing that calculates equivalent material constants inthe small regions, wherein the small region interior calculationprocessing calculates an area of each material included in the smallregion based on the shape data, obtains a slope of a line that expressesa boundary between the materials relative to a predetermined direction,and calculates an equivalent material constant for the small regionbased on the slope, the area, and the material constant data.

A storage medium storing an equivalent material constant calculationprogram according to the present invention allows a computer to executeprocessing that calculates an equivalent material constant of astructure constituted by a plurality of materials. The processingincludes shape data input processing that inputs shape data thatexpresses the shape of each material constituting the structure,material data input processing that inputs material constant data thatexpresses a material constant of at least one of the materialsconstituting the structure, dividing processing that divides thestructure expressed by the shape data into a plurality of small regions,representative material determining processing that determines amaterial that represents respective small regions for each of theplurality of small regions, material constant selection processing thatselects the material constant of the material that represents therespective small regions from the material constant data, and combiningprocessing that calculates an equivalent material constant for a regionin which a plurality of the small regions that are adjacent are combinedwith respect to at least one direction, by combining the materialconstant of the representative material of the plurality of adjacentsmall regions. Thus, with the equivalent material constant calculationprogram according to the present invention, it is possible to calculatean equivalent material constant that has taken into considerationanisotropy of the structure.

Hereinafter, the present invention will be described by way ofillustrative embodiments with reference to the drawings.

Embodiment 1

Embodiment 1 is an equivalent material constant calculation system inwhich an equivalent material constant of a structure constituted by aplurality of materials is calculated using an integral formula.

FIG. 1A is a functional block diagram that shows the configuration of anequivalent material constant calculation system of the presentembodiment. As shown in FIG. 1A, the equivalent material constantcalculation system 1 of the present embodiment includes a storageportion 2, a shape data input portion 3, a material data input portion4, a dividing portion 5, and a small region interior calculation portion6 the equivalent material constant calculation system 1 is connected toa CAD system 12 and an analysis system 13.

The equivalent material constant calculation system 1 can be constructedon, for example, general purpose equipment such as a personal computeror a workstation (hereinafter, referred to as ‘PC or the like’). Thefunction of the shape data input portion 3, the material data inputportion 4, the dividing portion 5, and the small region interiorcalculation portion 6 can be realized by the CPU of a PC or the likethat executes a predetermined program. As the storage portion 2, otherthan a storage medium built into a PC or the like such as a hard disk orRAM, a portable storage medium such as a floppy (registered trademark)disk or memory card, a storage medium in a storage device on a network,or the like can be used.

The equivalent material constant calculation system 1 can be constructedby, for example, installing the program that allows a computer toexecute the processing that is performed by the shape data input portion3, the material data input portion 4, the dividing portion 5, and thesmall region interior calculation portion 6 from a storage medium suchas a CD-ROM, or by download via a communications line, to a desired PCor the like.

The hardware configuration is not limited to the configuration shown inFIG. 1A. For example, the function of the equivalent material constantcalculation system 1 may be distributed to a plurality of PCs or thelike that have been connected by an internet or a LAN such thatcommunication is possible, for example. FIG. 1B is a functional blockdiagram that shows an example of the configuration of an equivalentmaterial constant calculation system in which the function of theequivalent material constant calculation system 1 is distributed to aterminal system 1 a and server system 1 b.

As shown in FIG. 1B, the terminal system 1 a includes, a shape datainput portion 3, a material data input portion 4, and a receivingportion 8. The server system 1 b includes a dividing portion 5, and asmall region interior calculation portion 6. The terminal system 1 a andthe server system 1 b are connected by an network 21 which is internetor intranet or the like for example. The terminal system 1 a can beconstructed on, for example, personal computer or the like which isconnected to the network 21. The server system 1 b can be constructedon, for example, server computer or the like which is connected to thenetwork 21.

The shape date input by the shape data input portion 3 and the materialdata input by the material data input portion 4 is send to the serversystem 1 b with requirement of calculation for a equivalent materialconstant. The dividing portion 5, and the small region interiorcalculation portion 6 included in the server system 1 b calculate aequivalent material constant base on the date send from the terminalsystem 1 a. the calculated equivalent material constant is send to theterminal system 1 a. the receiving portion 8 receives the equivalentmaterial constant which is send from the server system 1 b. According tothe configuration shown in FIG. 1B, the terminal system 1 a can obtainthe equivalent material constant without processing of calculating. Theterminal system 1 a may include the system of at least one of the CADsystem 12 and the analysis system 13.

The shape data input portion 3 inputs shape data of the structure forwhich an equivalent material constant will be calculated, and saves thatdata in the storage portion 2. The shape data, for example, is shapedata that expresses the shape of each material constituting thestructure. An electronic circuit board can be given as an example of thestructure. Ordinarily, shape data of an electronic circuit board oftenis created with a CAD system 12 for electronic circuit board design andsaved in the CAD system 12, so in this case information that is storedin a shape database 9 of the CAD system 12 can be used. Also, the shapedata input portion 3 may, for example, read a file in which the shapedata is stored to input new data, or the shape data input portion 3 mayreceive input of shape data that a designer created via an input devicesuch as a keyboard or a mouse provided in a PC or the like.

The material data input portion 4 inputs material constant data thatexpresses the material constants of the materials that constitute thestructure. An example of data that expresses a material constant, if thestructure is an electronic circuit board, is the material constant (forexample, such as a thermal conductivity or thermal resistance) of amaterial that constitutes the electronic circuit board. Materialconstant data of an electronic circuit board also can be used if thatinformation is saved in a material database 11 in the CAD system 12 forelectronic circuit board design. Also, the possibility of input via afile, keyboard, mouse, or the like is the same as for the shape datainput portion.

The dividing portion 5 divides the structure expressed by the shape datastored in the storage portion 2 into a plurality of small regions. Thesmall region interior calculation portion 6 calculates an equivalentmaterial constant for each of the divided small regions.

FIG. 2 is a functional block diagram that shows the configuration of thesmall region interior calculation portion 6. As shown in FIG. 2, thesmall region interior calculation portion 6 includes a boundary functiongenerating portion 61, a section setting portion 62, a section interiorcalculation portion 63, and an equivalent material constant generatingportion 64. These functions are described below.

Following is a description of the operation of the equivalent materialconstant calculation system 1 of the present embodiment with referenceto FIGS. 1 to 4. FIG. 3 is a flowchart that shows the operation of theequivalent material constant calculation system 1. In the presentembodiment, as one example, the processing that calculates theequivalent thermal conductivity of an electronic circuit board isdescribed. However, the present invention is not limited to anequivalent thermal conductivity calculation method of an electroniccircuit board or other structure. The present invention includescalculation methods for an equivalent electrical conductivity,equivalent dielectric constant, equivalent magnetic permeability,equivalent Young's modulus, or other material constants of compositematerials.

First, the shape data input portion 3 inputs shape data of the electriccircuit board for which the equivalent thermal conductivity calculationwill be performed (Step S21). The shape data of the electric circuitboard is created with a CAD system, for example. The electric circuitboard ordinarily is configured by alternately layering a wire layer andan insulation layer. FIG. 4 shows an example of the shape of a wirelayer included in the electronic circuit board for which the equivalentthermal conductivity calculation will be performed, and is a plan viewin a plane parallel to a layer of the electronic circuit board, i.e. inthe XY plane.

The wire layer of an electronic circuit board 101 is configured from awire pattern portion 103 and a non-wire portion 104. Ordinarily the wirepattern portion 103 is constituted by material with a comparatively highthermal conductivity such as metal, and the non-wire portion 104 oftenis constituted by material with a comparatively low thermal conductivitysuch as glass, resin, ceramics, or composites of these materials.

The material data input portion 4 inputs material constant data of thematerials that constitute the electronic circuit board 101 (Step S22).As material constant data, for example, the thermal conductivity(λtrace) of the wire material, which is metal material that constitutesthe wire pattern portion 103 of the electronic circuit board 101, andthe thermal conductivity (λinsulator) of the insulator material, whichis resin material that constitutes the non-wire portion 104, are input.Also, for example, because λinsulator is extremely small in comparisonto λtrace, in the subsequent equivalent thermal conductivity calculationprocessing, when it is possible to ignore λinsulator in the calculation,it is also possible to omit the input of λinsulator.

Because the shapes of the wire pattern portion 103 and the non-wireportion 104 that constitute the electronic circuit board 101 areextremely complicated, in order to simplify the subsequent processing,the dividing portion 5 divides the electronic circuit board 101 intolayers of each wire layer and insulation layer in the direction of the Zaxis, and divides each divided layer into small regions 102 in thedirection of the XY plane (Step S23). Division in the direction of the Zaxis can performed for each of the wire and insulation layers thatconstitute the electronic circuit board 101. With respect to division inthe direction of the XY plane, for example, as shown in FIG. 4, a layercan be divided into 11 equal divisions in the direction of the X axisand 10 equal divisions in the direction of the Y axis, dividing thewhole into 110 small regions. It is not necessary for the division intosmall regions to divide each direction in equal parts. It is alsopossible to divide into small regions with different sizes as necessary.

It does not matter if this division into the small regions 102 is thesame for each of the wire and insulation layers, or if it is different.Also, this division may be the same as the element division in acomputer simulation such as a finite element method performed using anequivalent thermal conductivity obtained by this method, for example, orit may be a dividing method that is different from this elementdivision.

Next, the small region interior calculation portion 6 calculates theequivalent thermal conductivity for each of these small regions 102(Step S24).

Here, in Step S24, the details of the processing that calculates anequivalent thermal conductivity for each small region 102 is describedwith reference to FIGS. 2, 5, and 6. FIG. 5 is a flowchart that showsthe detailed flow of processing that calculates an equivalent thermalconductivity for each small region 102 (Step S24).

First, the small region interior calculation portion 6 selects anddetermines the small region for which an equivalent thermal conductivitywill be calculated, from among the divided small regions 102 (Step S41).FIG. 6 shows an example of a selected small region 102. Next, the smallregion interior calculation portion 6 determines a direction u of thethermal conductivity to be calculated for the selected small region(Step S42). First, the direction u is made equal to the direction of theX axis. That is, an equivalent thermal conductivity of the X axisdirection will be calculated. It is preferable that the directions ofthe coordinate axes (X axis, Y axis, and Z axis) that will be thereference when calculating the equivalent thermal conductivity of thesmall region are set not only within the small region, but that commoncoordinate axes are set for the entire electric circuit board.

The small region 102 shown in FIG. 6 is configured from one wire patternportion 303 in the diagonal direction from the lower left to the upperright of the small region 102, and another, non-wire portion 304.

In the boundary function generating portion 61, a function thatexpresses an upper edge 31 (upper coordinate in the Y axis direction) ofthe wire pattern portion 303 with an X-Y coordinate system is madeY=F1(X), and a function that expresses a lower edge 32 (lower coordinatein the Y axis direction) of the wire pattern portion 303 with an X-Ycoordinate system is made Y=F2(X). However, because only the middle ofthe small region is handled, the domain of the function F1(X) is therange where X is X₁ to X₃, and the domain of the function F2(X) is therange where X is X₂ to X₄. F1(X) and F2(X) are functions that expressthe boundaries of the wire pattern portion 303 and the non-wire portion304. These functions are made based on the shape data that the shapedata input portion input.

The section setting portion 62, according to the domains of F1(X) andF2(X), sets a section in the small region 102 for X (S43-2). Forexample, it is possible to set the section X₂-X₃ where the domain ofF1(X) and the domain of F2(X) overlap to be section K1, set the sectionX₁-X₂ where only F1(X) is defined to be section K2, set the sectionX₃-X₄ where only F2(X) is defined to section K3, set the section X₀-X₁where both F1(X) and F2(X) are not defined to section K4, and set thesection X₄-X₅ to section K5.

Next, the section interior calculation portion 63 generates a functionthat expresses a material heat resistance Rd (S44) based on functionsF1(X), F2(X), and the material constant data of each material (λtraceand λinsulator).

For example, in section K1, when ΔX is made the minimum range of X₂ toX₃, a heat resistance Rc in the X axis direction of a minimum regionexpressed by a width in the X axis direction of ΔX and a length in the Yaxis direction of c is approximated by ΔX/(λinsulator·c·t). A heatresistance Rb in the X axis direction of a minimum region expressed by awidth in the X axis direction of ΔX and a length in the Y axis directionof b is approximated by ΔX/(λtrace·b·t), and a heat resistance Ra in theX axis direction of a minimum region expressed by a width in the X axisdirection of ΔX and a length in the Y axis direction of a isapproximated by ΔX/(λinsulator·a·t). Here t expresses the thickness ofthe wire pattern portion 303 in a direction perpendicular to the XYplane.

Here, when the X coordinate of the left end of ΔX is made Xd, and thelength in the Y axis direction of the small region 102 is made Y1,a=Y1=F1(Xd), b=F1(Xd)·F2(Xd), and c=F2(Xd), so when using this a, b, andc, the above Ra, Rb, and Rc are indicated by formula 5, formula 6, andformula 7, respectively.

$\begin{matrix}{{Ra} = \frac{\Delta\; X}{\lambda\;{{insulator}\left( {{Y\; 1} - {F\; 1({Xd})}} \right)}t}} & {{Formula}\mspace{20mu} 5} \\{{Rb} = \frac{\Delta\; X}{{\lambda\;{{trace}\left( {{F\; 1({Xd})} - {F\; 2({Xd})}} \right)}t}\mspace{14mu}}} & {{Formula}\mspace{14mu} 6} \\{{Rc} = \frac{\Delta\; X}{\lambda\;{insulator}\mspace{14mu} F\; 2({Xd})t}} & {{Formula}\mspace{14mu} 7}\end{matrix}$

where the thermal conductivity of the material that constitutes the wirepattern portion 303 is λtrace, and the thermal conductivity of thematerial that constitutes the non-wire portion 304 is λinsulator.

In the range where the X axis direction is ΔX and the Y axis directionis the entire small region 102, when considering the thermal resistancein the X axis direction, it is possible to consider the three thermalresistances, whose respective thermal resistance values are Ra, Rb, andRc, to be connected in parallel, and so the thermal resistance Rd of thewhole is shown by formula 8.

$\begin{matrix}\begin{matrix}{\mspace{79mu}{\frac{1}{Rd} = {\frac{1}{Ra} + \frac{1}{Rb} + \frac{1}{Rc}}}} \\{= {\frac{\lambda\;{{insulator}\left( {{Y\; 1} - {F\; 1({Xd})}} \right)}t}{\Delta\; X} +}} \\{\frac{\lambda\;{{trace}\left( {{F\; 1({Xd})} - {F\; 2({Xd})}} \right)}t}{\Delta\; X} +} \\{\frac{\lambda\;{insulator}\mspace{14mu} F\; 2({Xd})t}{\Delta\; X}} \\{= \frac{G}{\Delta\; X}}\end{matrix} & {{Formula}\mspace{14mu} 8} \\{G = {{\lambda\;{{insulator}\left( {{Y\; 1} - {F\; 1({Xd})}} \right)}t} + {\lambda\;{{trace}\left( {{F\; 1({Xd})} - {F\; 2({Xd})}} \right)}t} + {\lambda\;{insulator}\mspace{14mu} F\; 2({Xd})t}}} & \;\end{matrix}$

Formula 8 above is a function that expresses the thermal resistance Rdin the minimum region ΔX. Here, the function shown by the formula 8 isan example of a function that expresses a position where the materialconstant is applied. Next, the section interior calculation portion 63,by integrating this function within the section K1, obtains anequivalent thermal resistance in the X axis direction for the section K1(S45).

The equivalent thermal resistance in the X axis direction of the sectionK1(X₂-X₃) in which both F1(X) and F2(X) are defined can be obtained byreducing the width of ΔX to a limit and integrating Rd in the X axisdirection from X₂ to X₃, and that value Rx1 is shown by formula 9.

$\begin{matrix}{\begin{matrix}{\mspace{79mu}{{{Rx}\; 1} = {\int_{X\; 2}^{X\; 3}{R\ \mathbb{d}}}}} \\{= {\int_{X\; 2}^{X\; 3}{\frac{1}{G}\ {\mathbb{d}x}}}}\end{matrix}{G = {{\lambda\;{{insulator}\left( {{Y\; 1} - {F\; 1({Xd})}} \right)}t} + {\lambda\;{trace}\left( {{F\; 1({Xd})} - {F\; 2({Xd})}} \right)t} + {\lambda\;{insulator}\mspace{14mu} F\; 2({Xd})t}}}} & {{Formula}\mspace{14mu} 9}\end{matrix}$

In the above manner, it is possible to obtain the equivalent thermalresistance in the X axis direction of the section K1 by using thefunctions F1(X) and F2(X) that express the boundary to form a function(above formula 8) that expresses the thermal resistance of the minimumregion ΔX, and integrating this function in the section K1. Accordingly,provided that it is possible to solve functions F1(X) and F2(X), even ifthe shape of the material is complicated, it is possible to obtain anequivalent thermal resistance with good effectiveness without increasingthe processing time and the amount of processing logic.

That is, for each material, by integrating a function (the above formula8) that includes the product of the size in a particular direction (Yaxis direction) of that material and the material constant of thatmaterial, with a direction (X axis direction) that differs from theabove dimensional direction (Y axis direction), it is possible to obtainan equivalent thermal resistance in the X axis direction.

However, in the present invention, integration does not have only therigorous mathematical meaning of that word; it includes various kinds ofnumerical integration performed with a computer using, for example, atrapezoidal approximation method, Simpson method, Gauss-Legendre method,or various other types of approximation methods.

Also, in the present embodiment, calculation was performed taking intoconsideration the thermal conductivity of both the wire pattern portion303 and the non-wire portion 304, but when the thermal conductivityλinsulator of the material that constitutes the non-wire portion 304 isvery small in comparison to the thermal conductivity λtrace of thematerial that constitutes the wire pattern portion 303, it is possibleto lighten the calculation load by ignoring the thermal conductivityeffect of the insulator material that constitutes the non-wire portion.

Also, in the present embodiment, calculation was performed with boundaryfunctions F1(X) and F2(X) as functions that express boundary lines ofthe XY plane, but calculation also may be performed by generatingboundary functions as functions that express boundary planes of thespace XYZ.

In the above, a method was described that calculates the equivalentthermal resistance in the X axis direction of the section K1, here, acorrection example that is preferable in the above calculation methodwill be described. FIG. 7 shows a condition in which heat is transmittedin the section K1 of the small region 102 shown in FIG. 6. The arrows inFIG. 7 show the flow of heat. In the calculation method described above,as shown in FIG. 7A, calculation is performed with the assumption thatheat is transmitted parallel to the X axis direction. However, from theresults of heat analysis and the like, as in FIG. 7B, it is known thatheat flows parallel to the direction of the wire pattern portion 303.Consequently, in the above calculation method, it is preferable toperform correction that takes into account the actual flow of heat.

Specifically, as shown in FIG. 8, when the interval of the integratedsection of the wire in the above calculation method prior to correctionis f, and the heat path width is g, an actual wire heat path lengthf_(t) is f_(t)=f/sin θ, and a heat path width g_(t) is g_(t)=g sin θ.Considering that in this way, in actuality, the heat path lengthincreases and the heat path width narrows, it is preferable to correctthe thermal conductivity λtrace of the wire pattern portion 303.Specifically, in the above formula 6, formula 8, and formula 9, byperforming the calculation with λtrace replaced by an apparent thermalconductivity sin² θ*λtrace, calculation of a highly accurate equivalentthermal conductivity becomes possible.

As stated above, an equivalent thermal resistance Rx1 in the X axisdirection for the section K1 shown in FIG. 6 is calculated. Likewise,thermal resistances Rx2 to Rx5 are calculated respectively in the X axisdirection for sections K2 to K5. The processing of Steps S44 to S45shown in FIG. 5 is repeated until the processing that obtains theequivalent thermal resistances Rx1 to Rx5 in the X axis direction forall of the sections K1 to K5 is completed.

In Step S46, when it is judged that the equivalent thermal resistancesRx1 to Rx5 in the X axis direction have been calculated for all of thesections of the small region 102, the equivalent material constantgenerating portion 64 generates an equivalent thermal resistance Rx inthe X axis direction for the entire small region 102. The equivalentthermal resistance Rx in the X axis direction for the entire smallregion 102 is expressed by the sum of the equivalent thermal resistancesRx1 to Rx5 of the regions K1 to K5 (see formula below), because it ispossible to consider the equivalent thermal resistances Rx1 to Rx5 ofthe regions K1 to K5 to be connected in series.Rx=ΣRxi (Σ is the summation of i=1, 2, 3, 4, 5)

An equivalent thermal conductivity λX in the X axis direction of thesmall region 102 in the direction of XY plane is expressed byλx=Lx/(Rx·Ly·t), where Lx is the size in the X axis direction of thesmall region 102, Ly is the size in the Y axis direction, and t is thesize (thickness) in the direction perpendicular to the XY plane.

When the equivalent thermal conductivity λx in the X axis direction iscalculated, again in Step S42, the coordinate axis direction u of thecalculation target is made the Y axis direction. Afterwards, bysimilarly repeating the processing in Step S43 to Step S47, anequivalent thermal conductivity λy in the Y axis direction of the smallregion 102 is calculated. When the equivalent thermal conductivity λx inthe X axis direction and the equivalent thermal conductivity λy in the Yaxis direction have been calculated, when the equivalent materialconstant generating portion 64 performs judgment (S48), again in StepS41, the small region interior calculation portion 6 next selects a newsmall region, and performs equivalent thermal conductivity calculationprocessing for the selected region (S49).

By performing the above processing for all of the small regions on theelectronic circuit board 101, an equivalent thermal conductivity in theX axis direction and an equivalent thermal conductivity in the Y axisdirection are calculated for each of the small regions. The calculateddata is saved in the storage portion 2 (S25 in FIG. 3).

When an analysis system 13 performs, for example, thermal analysis orthe like of the electronic circuit board 101, the equivalent thermalconductivities are used by reading them from the storage portion 2.

According to the present embodiment, both an equivalent thermalconductivity in the X axis direction and an equivalent thermalconductivity in the Y axis direction is obtained for each of the smallregions. Thus, for example, for each of the small regions, anisotropy ofthe thermal conductivity is identified in the X and Y directions, inwhich heat is easily transmitted in the X axis direction but not easilytransmitted in the Y axis direction. That is, equivalent thermalconductivities are obtained that have taken into consideration thedirectionality of the materials that constitute the electronic circuitboard. As a result, at the same time that the calculation accuracy ofthe equivalent material constants is dramatically improved, it ispossible to also realize a reduction in the calculation time.

This method of calculating an equivalent thermal conductivity, which isa first embodiment of the present invention, can be expressed by beingstored as steps of a program executable by a computer.

This program executable by a computer is one embodiment of theequivalent material constant calculation program of the presentinvention.

Also, this program executable by a computer requires that data necessaryto execute the processing of the program be input externally, such asfrom user operation for example, and also may include a prompting stepto for such input, and a step to execute that input.

A program executable by a computer that includes these sorts of steps isalso one embodiment of the equivalent material constant calculationprogram of the present invention.

Also, these programs executable by a computer are stored on a recordingmedium that can be read by a computer, and this recording medium is oneembodiment of a recording medium on which the equivalent materialconstant calculation program of the present invention is stored.

Further, the recording medium that can be read by a computer on whichthis program executable by computer is stored, and the computer, alongwith any number of other constituent elements, constitute an equivalentthermal conductivity calculation device, and this is one embodiment ofthe equivalent material constant calculation device.

Embodiment 2

Following is a description of another embodiment of the presentinvention. Embodiment 2 is an equivalent material constant calculationsystem that calculates an equivalent material constant of a structureconstituted by a plurality of materials, using an FFT method statedlater.

The configuration of the equivalent material constant calculation systemof the present embodiment is the same as the functional block diagramshown in FIG. 1A, except for the points stated below, so that theexplanation thereof will be omitted here. The operation of theequivalent material constant calculation system of the presentembodiment is the same as the flowchart shown in FIG. 3, except for thepoints stated below, so that explanation thereof also will be omittedhere.

The processing of the system in the present embodiment differs from theprocessing of the system in Embodiment 1 in that the equivalent materialconstant calculation processing for the small region (Step S24) isdifferent. Below, the equivalent material constant calculationprocessing for the small region in the present embodiment will bedescribed with reference to FIG. 9 and FIG. 10.

FIG. 9 is a functional block diagram that shows the configuration of thesmall region interior calculation portion 6 in the present embodiment.As shown in FIG. 9, the small region interior calculation portion 6includes a minimum region material constant generating portion 65, aspectrum calculation portion 66, and an equivalent material constantgenerating portion 67.

FIG. 10 is a flowchart that shows the detailed flow of processing thatcalculates an equivalent thermal conductivity for each small region 102in the present embodiment.

First, the small region interior calculation portion 6 selects anddetermines the small region for which an equivalent thermal conductivitywill be calculated, from among the divided small regions 102 (Step S51).FIG. 11 shows an example of a selected small region 102.

The small region 102 shown in FIG. 11 is configured from three wirepattern portions lined up with a fixed interval in the X axis direction(the portion of the non-wire portion 404), and each wire pattern portion403 has a shape that continues in the Y axis direction. That is, theshape occupied by the wire pattern portions 403 in the small region 102is a shape that is repeatedly distributed, with a high frequency (shortwavelength) in the X axis direction and a low frequency in the Y axisdirection (long wavelength).

In order to measure this quantitatively, the minimum region materialconstant generating portion 65, as shown in FIG. 11, again divides thesmall region 102 into small minimum regions (Step S52). For example, thesmall region 102 is divided into M-regions of 0 . . . m . . . M−1 in theX axis direction, and N-regions of 0 . . . n . . . N−1 in the Y axisdirection. These respective minimum regions are made a minimum region(m, n).

Next, the minimum region material constant generating portion 65 definesa function that associates 1 or 0 with each minimum region (m, n)according to whether or not a wire pattern portion 403 is present inthat minimum region (m, n). Alternatively, it defines a function f(m, n)for each minimum region (m, n) that associates an area ratio of the wirepattern portion 403 included in that minimum region (m, n).

For example, when a wire pattern portion 403 is present in the minimumregion (0, 0), and the area ratio of that region is half or more, afunction f(0, 0)=1 may be defined. Alternatively, the area ratio for theentire minimum region of the wire pattern portion 403 in the minimumregion may be made the value of the function f. For example, when a wirepattern portion 403 is present in the minimum region (0, 0) and the arearatio of that region is about 0.9, a function f(0, 0)=0.9 may bedefined.

Also, the function may be defined by more rigorously calculating thearea ratio of the wire pattern portion 403 occupied in each minimumregion and making that area ratio the value of f(m, n), or the functionmay defined by making the value of f(m, n) 1 or 0, depending on whetheror not the area ratio of the wire pattern portion 403 occupied in eachminimum region exceeds a specific threshold value (for example, 0.5 or0.8).

Next, the minimum region material constant generating portion 65calculates an equivalent thermal conductivity λ′(m, n) of this minimumregion (m, n) (Step S53). This equivalent thermal conductivity λ′(m, n)of the minimum region (m, n) is made a provisional equivalent thermalconductivity λ′(m, n). The calculation of λ′(m, n) can be performedusing, for example, formula 10. In formula 10, λtrace is the thermalconductivity of the material that constitutes the wire pattern portion403, and λinsulator is the thermal conductivity of the material thatconstitutes the non-wire portion 404.λ′(m,n)=λtracef(m,n)+λinsulator(1−f(m,n))  Formula 10Also, λ′(m, n) may be calculated by applying, for example, the method ofgenerating the equivalent material constant of the small region inEmbodiment 1, that is, a method that integrates a function thatexpresses the boundaries of the wire pattern portion 403 and thenon-wire portion 404.

Next, the frequency spectrum of the distribution status in the X axisdirection and the Y axis direction of the provisional equivalent thermalconductivity λ′(m, n) that accompanies the distribution profile of thewire pattern portion 403 in the small region 102, i.e. the frequencycomponents, are calculated (Step S54). Specifically, a spectrumcalculation portion 66 performs a two-dimensional discrete Fouriertransformation for λ′(m, n), and obtains each frequency component c (m,n) (frequency components corresponding to 2 πm/M in the X axisdirection, and corresponding to 2 πn/N in the Y axis direction).

This formula that calculates frequency components c(m, n) is shown informula 11. In formula 11, i expresses a complex number.

$\begin{matrix}{{c\left( {m,n} \right)} = {\sum\limits_{y = 0}^{N - 1}{\sum\limits_{x = 0}^{M - 1}{\Delta\;{x \cdot {\exp\left( {{- 2}\;\pi\;{{imy}/N}} \right)} \cdot \Delta}\;{y \cdot {\exp\left( {{- 2}\;\pi\;{{inx}/M}} \right)} \cdot {\lambda^{\prime}\left( {x,y} \right)}}}}}} & {{Formula}\mspace{14mu} 11}\end{matrix}$

Based on the frequency components c(m, n), the equivalent materialconstant generating portion 67 obtains respective equivalent thermalconductivities λequivalent, X and λequivalent, Y for the X axisdirection and the Y axis direction of the entire small region 102 (StepS55). The respective equivalent thermal conductivities λequivalent, Xand λequivalent, Y for the X axis direction and the Y axis direction ofthe entire small region 102 are obtained by calculating the sum of thefrequency components c(m, n), which have been weighted. Specifically,they can be obtained by calculating the weighted sum of the powers to befixed for the frequency components c(m, n) of the provisional equivalentthermal conductivity λ′(m, n). This formula is shown in formula 12 andformula 13.

$\begin{matrix}{{\lambda\;{equivalent}},{X = {\sum\limits_{r}{\sum\limits_{m}{\sum\limits_{n}{\alpha_{mnr}\left( {c\left( {m,n} \right)} \right)}^{r}}}}}} & {{Formula}\mspace{14mu} 12} \\{{\lambda\;{equivalent}},{Y = {\sum\limits_{r}{\sum\limits_{m}{\sum\limits_{n}{\beta_{mnr}\left( {c\left( {m,n} \right)} \right)}^{r}}}}}} & {{Formula}\mspace{14mu} 13}\end{matrix}$

The power r and the weights (α and β) of the weighted sum are valuesdetermined by advance testing or a logical method. For example, it ispossible to perform the calculation with α and β as constants only wherer=1. Similarly, it is possible to perform the calculation with α and βas constants only where r=2, only where r=3, only where r=−1, only wherer=−2, or only where r=−3. Also, for example, the weighted sum may bycalculated where r=1 to 3 (for example, α=α₁, α₂, α₃, β=β₁, β₂, β₃). Aweighted sum of r=2 to 10, a weighted sum of only odd-numbered powersr=−5 to +5, or a weighted sum of various other powers can be used.

An equivalent thermal conductivity in the X axis direction and the Yaxis direction of the small region 102 can be calculated in the abovemanner.

In the present embodiment, in the above formula 11, using atwo-dimensional discrete Fourier transformation, a frequency spectrumwas obtained for the material constants in the X and Y directions, butit is also possible to obtain a frequency spectrum using thedistribution of material constants in a three-dimensional space, i.e. inthe X, Y, and Z directions, using a three-dimensional discrete Fouriertransformation.

Embodiment 3

Following is a description of another embodiment of the presentinvention. Embodiment 3 is an equivalent material constant calculationsystem that calculates an equivalent material constant of a structureconstituted by a plurality of materials.

The configuration of the equivalent material constant calculation systemof the present embodiment is the same as the functional block diagramshown in FIG. 1A, except for the points stated below, so that theexplanation thereof will be omitted here. The operation of theequivalent material constant calculation system of the presentembodiment is the same as the flowchart shown in FIG. 3, except for thepoints stated below, so that the explanation thereof will also beomitted here.

The processing of the system in the present embodiment differs from theprocessing of the system in Embodiment 1 in that the equivalent materialconstant calculation processing for the small region (Step S24) isdifferent. Below, the equivalent material constant calculationprocessing for the small region in the present embodiment will bedescribed with reference to FIG. 12 and FIG. 13.

FIG. 12 is a flowchart that shows the detailed flow of processing thatcalculates an equivalent thermal conductivity for the small region 102in the present embodiment.

First, the small region interior calculation portion 6 selects anddetermines the small region for which an equivalent thermal conductivitywill be calculated, from among the divided small regions 102 (Step S61).FIG. 13A shows an example of a selected small region 102.

In the small region 102 shown in FIG. 13A, a trapezoidal portion withvertexes is the wire pattern portion, and the other portions are thenon-wire portions. The wire pattern portions, are, for example,constituted by material such as copper, and the non-wire portions, are,for example, constituted by material such as epoxy.

The small region interior calculation portion 6 calculates the area ofthe trapezoid ABCD (Step S61). The coordinates of these trapezoidvertexes ABCD, for example, are expressed by the shape data that hasbeen input with the shape data input portion 3. Thereby the area of thewire pattern portions is obtained.

Next, the small region interior calculation portion 6 obtains a sloperelative to the X axis direction of a line that indicates a boundarybetween a wire pattern portion and a non-wire portion (Step 563). Theslope is indicated by an angle, for example. In the example shown inFIG. 13A, an angle θ1 of the boundary line AD relative to the X axis,and an angle θ2 of the boundary line BC relative to the X axis areobtained. The small region interior calculation portion 6 also obtainsan average value θav of these angles θ1 and θ2. The average value θav,for example, is a value of the arithmetic mean of angles θ1 and θ2.

The small region interior calculation portion 6 obtains an equivalentthermal conductivity λequivalent for the small region 102 using theaverage value θav, the material constant λtrace of the material thatconstitutes the wire pattern portions, and the area of the wire patternportions.

The equivalent thermal conductivity λequivalent, for example, isexpressed as in formula 14. In formula 14, the area ratio of the wirepattern portions in the small region 102 is made α, and the area ratioof the non-wire portions in the small region 102 is made (1−α). Also,the material constant of the material of the non-wire portions is madeλinsulator.λequivalent=sin² θ_(av)·λtrace·α+λinsulator·(1−α)  Formula 14

In formula 14 above, by multiplying λtrace by sin² θav and addingcorrection, the material constant in the Y axis direction of the smallregion 102 is calculated. That is, with a simple calculation, a materialconstant that takes directionality into consideration is obtained. Whenobtaining a material constant in the X axis direction of the smallregion 102, for example, it is preferable to obtain the slope relativeto the Y axis of the boundary line between each material. By making theaverage value of the slope relative to the Y axis θav and substitutingin above formula 14, it is possible to obtain a material constant in theX axis direction.

The average value θav is not limited to the arithmetic mean of theangles θ1 and θ2. For example, it is possible to make a geometric meanvalue of the angles θ1 and θ2 the average value θav. Or, for example,maximum and minimum values may be used in place of an average value.

FIG. 13B shows an example of equivalent material constants for the smallregion 102 calculated respectively using an arithmetic mean, geometricmean, maximum value, and minimum value as θav.

In this table, “precise analysis value” is an equivalent materialconstant calculated using a finite element method with sufficientaccuracy to obtain a value close to reality.

The value of “no correction” is an equivalent material constant obtainedbased on the area ratio of the wire pattern portion and the non-wireportion without taking into consideration the slope of boundary lines.That is, the value of “no correction” is an equivalent material constantcalculated without using sin² θav in formula 14.

The value of “maximum value” is an equivalent material constantcalculated using the maximum values of the angles θ1 and θ2 for θav informula 14. The value of “minimum value” is an equivalent materialconstant calculated using the minimum values of the angles θ1 and θ2 forθav.

The value of “arithmetic mean” is an equivalent material constantcalculated using the arithmetic average of the angles θ1 and θ2 for θav.The value of “geometric mean” is an equivalent material constantcalculated using the geometric mean of the angles θ1 and θ2 for θav.

In the table shown in FIG. 13B, the percentage of each value when the“precise analysis value” is made 100% is also shown. From this chart, itis understood that the weighted average value and the arithmetic averagevalue are extremely close to the precise analysis value.

Embodiment 4

Following is a description of another embodiment of the presentinvention. Embodiment 4 is an equivalent material constant calculationsystem that, using a proportional allocation method, calculates anequivalent material constant of individual solids included in astructure constituted from a plurality of materials, and also calculatesan equivalent material constant for a region in which this plurality ofsolids has been combined.

FIG. 14 is a functional block diagram that shows an example of aconfiguration of an equivalent material constant calculation system 10of the present embodiment. In the block diagram shown in FIG. 14, thesame numerals are attached to the same blocks as the block diagram shownin FIG. 1A, and their explanation is not repeated.

The block diagram shown in FIG. 14 differs from FIG. 1A in that acombined portion 7 is provided. The combined portion 7 includes alamination direction combining portion 71 and a perpendicular directioncombining portion 72. The lamination direction combining portion 71obtains an equivalent material constant of a region in which the smallregions divided by the dividing portion 5 are combined in the laminationdirection. The perpendicular direction combining portion 72 obtains anequivalent material constant of a region in which adjacent small regionshave been combined in the direction perpendicular to the laminationdirection of the small regions.

FIG. 15 is a flowchart that shows the operation of the equivalentmaterial constant calculation system of the present embodiment. In theflowchart shown in FIG. 15, the same numerals are attached to steps thatare the same as in the flowchart shown in FIG. 3, and their explanationis not repeated.

The flowchart shown in FIG. 15 is different from FIG. 3 in that theprocessing of Step S35 and Step S36 is newly added. Also, the processingthat obtains equivalent material constants for each small region in FIG.15 (S34) is different from the processing that obtains equivalentmaterial constants for each small region in FIG. 3. First, the detailsof the processing in Step S34 will be described.

First, the small region interior calculation portion 6 selects anddetermines the small region for which an equivalent thermal conductivitywill be calculated, from among the divided small regions 102. FIG. 16shows an example of a selected small region 102.

This selected small region 102 is constituted from a portion that is around wire pattern portion 203 that occupies about ¼ of the area of theentire small region 102, a portion that is a wire pattern portion 203that is a thin lead line drawn out from the round portion, and anon-wire portion 204, which is the remaining portion of the small region102.

The position and diameter of the round wire pattern portion 203 portionand position, width, length, and the like of the thin lead line wirepattern portion 203 portion are stored in the storage portion 2 as theshape data input by the shape data input portion. So when prescribingthe position coordinates, the length in the X axis direction and thelength in Y axis direction of this small region 102, it is possible tocalculate directly the area of the wire pattern portions 203 and thearea of the non-wire portion 204 in this small region 102, and the arearatio of these ratios.

The area ratio of the wire pattern portions 203 in the small region 102is made α, and the area ratio of the non-wire portion 204 in the smallregion 102 is made (1−α). The thermal conductivity of the material thatconstitutes the wire pattern portions 203 is made λtrace, and thethermal conductivity of the material that constitutes the non-wireportion 204 is made λinsulator. The thermal conductivity λequivalent ofthe small region 102 is expressed as in formula 15.λequivalent=λtraceα+λinsulator(1−α)  Formula 15

Regarding the thermal conductivity λequivalent expressed in the aboveformula 15, the thermal conductivity in the X axis direction and thethermal conductivity in the Y axis direction are not necessarilydistinguished. For example, it is possible to consider the thermalconductivity in the X axis direction and the thermal conductivity in theY axis direction as having the same λequivalent.

Thus anisotropy is not taken into consideration in the thermalconductivity λequivalent, and it has low accuracy. In order to increaseaccuracy, it is necessary to divide the electronic circuit board morefinely, and obtain equivalent material constants for a greater number ofsmall regions. However, when the number of small regions is large, thenumber of output equivalent material constants also increases to thatextent. As a result, analysis processing also becomes difficult whenperforming analysis using the output equivalent material constants, andefficiency worsens.

Consequently, it becomes necessary to decrease the amount of outputdata, while maintaining a particular level of accuracy for theequivalent material constants. Therefore, in the present embodiment,processing (S35 and S36) is provided that obtains an equivalent materialconstant for a region in which a plurality of adjacent small regionshave been combined.

Following is a description of this processing (S35 and S36). By addingthis processing after Step S24 in the flowchart shown in FIG. 3, it canbe applied to Embodiment 1, Embodiment 2, and Embodiment 3 also. Thus,the processing below is described assuming that the thermal conductivityλequivalent in the X axis direction and the thermal conductivityλequivalent in the Y axis direction both have been obtained for thesmall region 102, as in the case of Embodiment 1-3.

In Step S34, when the equivalent thermal conductivity of each smallregion 102 is calculated, the lamination direction combining portion 71obtains the thermal conductivity in the X axis direction and the thermalconductivity in the Y axis direction, for a region in which smallregions for layers that have been layered in the Z axis direction havebeen combined in the lamination direction (Step S35).

Following is a description of the processing of Step S35, that is,processing that obtains an equivalent thermal conductivity for a regionin which the small regions of each layer have been combined in thelamination direction.

FIG. 17 is a cross-sectional diagram in plane XZ, when the electroniccircuit board 101 is divided into seven layers in the Z axis direction,the divided layers are further divided into small regions 102 in the XYplane, and a cross section including one of these further divided smallregions 102 is viewed from the Y axis direction in a three-dimensionalspace.

This cross section including the small regions 102, when viewed as across-sectional diagram in the XZ plane, includes the small regions ofseven layers parallel to the XY plane laminated in the Z axis direction.Those small regions of seven layers, beginning from the small regionwith the upper coordinates in the Z axis direction, are a wire layer521, an insulation layer 532, a wire layer 523, an insulation layer 534,a wire layer 525, an insulation layer 536, and a wire layer 527, whoserespective thicknesses are t1, t2, t3, t4, t5, t6, and t7.

The respective wire layers 521, 523, 525, and 537 are configured fromthe wire pattern portion 503 and the non-wire portion 504, and the wirepattern portion ordinarily is made of metal material or the like. Thenon-wire portion 504 may be made from an insulator portion 511, or maybe a space in which there is nothing.

The respective insulation layers 532, 534, and 536 are configured by theinsulator portion 511, but metal material or the like that constitutesthe wire pattern portion 503 (such as a through-hole 512) also may beincluded in a portion thereof.

The equivalent thermal conductivity in the X axis direction of the smallregion of a layer No. i (i=1, 2, . . . 7) of the seven layers is madeλequivalent,X,i, and the equivalent thermal conductivity in the Y axisdirection of the small region of the layer No. i is madeλequivalent,Y,i, and when the X axis direction and the Y axis directionare not particularly distinguished, their equivalent thermalconductivity is expressed by λequivalent,i. When doing so, an equivalentthermal resistance Requivalent,X,i in the X axis direction for the unitwidth (unit measurement in the Y axis direction) of the layer No. i isexpressed by the reciprocal of the equivalent thermal conductivityλequivalent,X,i.Requivalent,X,i=1/(λequivalent,X,i·ti)Likewise, the equivalent thermal resistance Requivalent,Y,i in the Yaxis direction of the layer No. i is 1/(λequivalent,Y,i·ti).

It is possible to consider that, when viewing the region in which thesmall regions of the seven small layers are all combined in thelamination direction (Z axis direction) from the X axis direction or theY axis direction, the small regions of the seven layers (i=1 to 7) withequivalent thermal resistance Requivalent,i are connected in parallel.Accordingly, the equivalent thermal resistance Requivalent of the regionin which the small regions 102 have been combined across all layers inthe Z axis direction is expressed by formula 16.

$\begin{matrix}{{\frac{1}{R\;{equivalent}} = {\sum\limits_{i}{\lambda\;{equivalent}}}},{i \cdot t_{i}}} & {{Formula}\mspace{14mu} 16}\end{matrix}$

The equivalent thermal conductivity λequivalent in the X axis directionand the Y axis direction of a three-dimensional region in which thesmall regions 102 are combined across all layers in the Z axis directioncan be calculated by dividing the reciprocal of the equivalent thermalresistance Requivalent expressed in formula 16 by an entire thicknessLz, and so it is expressed by formula 17.

$\begin{matrix}{{\lambda\;{equivalent}} = \frac{{\sum\limits_{i}{\lambda\;{equivalent}}},{i \cdot t_{i}}}{lz}} & {{Formula}\mspace{14mu} 17}\end{matrix}$

This formula in which the X axis direction and the Y axis direction aredistinguished is expressed in formula 18 and formula 19.

$\begin{matrix}{{\lambda\;{equivalent}},{X = \frac{{\sum\limits_{i}{\lambda\;{equivalent}}},X,{i \cdot t_{i}}}{lz}}} & {{Formula}\mspace{14mu} 18} \\{{\lambda\;{equivalent}},{Y = \frac{{\sum\limits_{i}{\lambda\;{equivalent}}},Y,{i \cdot t_{i}}}{lz}}} & {{Formula}\mspace{14mu} 19}\end{matrix}$

As described above, in Step S35, it is possible to calculate theequivalent thermal resistance Requivalent,X in the X axis direction andthe equivalent thermal resistance Requivalent,Y in the Y axis directionof a three-dimensional region in which the small regions 102 arecombined across all layers in the lamination direction.

Next, based on the equivalent thermal resistance Requivalent obtained inStep S35, the perpendicular direction combining portion 72 obtains anequivalent material constant for a region in which a plurality ofadjacent regions are combined (Step S36).

FIG. 18, for example, is a plan view showing four adjacent small regions601, 602, 603, and 604 from the Z axis direction.

The small region 601, for example, in Step S35, is a three-dimensionalregion in which the small regions 102 are combined across all layers inthe lamination direction. In that case, the small region 601 has theequivalent thermal resistance Requivalent,X in the X axis direction andthe equivalent thermal resistance Requivalent,Y in the Y axis direction.Similarly, the other three small regions 602, 602, and 604 arethree-dimensional regions in which the small regions 102 are combinedacross all layers in the lamination direction, respectively having anequivalent thermal resistance in the X axis direction and an equivalentthermal resistance in the Y axis direction.

Here, one small region 601 is expressed by a square with a center of,for example, n1. For the equivalent thermal resistance in the X axisdirection of the small region 601, it is possible to consider R12 andR14 as being connected in series. R12 and R14 have the relationshipshown in the formula below. In the below formula, 0<α<1.R14=Requivalent,X·αR12=Requivalent,X·(1−α)The value of αis ordinarily 0.5, but it can be changed according tocircumstances.

Likewise, for the equivalent thermal resistance in the Y axis directionof the small region 601, it is possible to consider R11 and R13 as beingconnected in series. This is also true for the other small regions 602,603, and 604.

The equivalent thermal resistance in the X axis direction of the regionin which the four small regions 601, 602, 603, and 604 can be consideredto be a thermal resistance between n0 and n5. Also, because it ispossible to consider that for the thermal resistance of the entirecombined region, the thermal resistances R11 to R14, R21 to R24, R31,and R41 to R44 of the small regions 601, 602, 603, and 604 are connectedas shown in FIG. 18, the thermal resistance between n0 and n5 can becalculated using Kirchoff's law in the calculation of electricalresistance. When the thermal resistance between n0 and n5 is calculatedusing Kirchoff's law in the calculation of electrical resistance, it ispossible to use a matrix operation.

Here, an example of calculating the thermal resistance between n0 and n5using Kirchoff's law is explained. In FIG. 18, the electrical potentialsin nodes n0, n1, n2, n3, n4, and n5 are respectively made V1, V2, V3,V4, and V5. Here, because the sum of current that enters ni is 0,formulas 20 to 24 are satisfied. For example, the sum of current thatenters node n0 is expressed by the left side of below formula 20, andthis is 0. Likewise, formula 21 is satisfied at node n1, formula 22 issatisfied at node n2, formula 23 is satisfied at node n3, formula 24 issatisfied at node n4, and formula 25 is satisfied at node n5. Here, thecurrent that enters node n0 is made I₀, and the current that enters noden5 is made I₅.

$\begin{matrix}{{\frac{V_{1} - V_{0}}{R\; 14} + \frac{V_{4} - V_{0}}{R\; 44} + I_{0}} = 0} & {{Formula}\mspace{14mu} 20} \\{{\frac{V_{1} - V_{0}}{R\; 14} + \frac{V_{4} - V_{1}}{{R\; 13} + {R\; 41}} + \frac{V_{2} - V_{1}}{{R\; 12} + {R\; 24}}} = 0} & {{Formula}\mspace{14mu} 21} \\{{\frac{V_{2} - V_{1}}{{R\; 24} + {R\; 12}} + \frac{V_{5} - V_{2}}{R\; 22} + \frac{V_{3} - V_{2}}{{R\; 31} + {R\; 23}}} = 0} & {{Formula}\mspace{14mu} 22} \\{{\frac{V_{3} - V_{2}}{{R\; 31} + {R\; 23}} + \frac{V_{3} - V_{4}}{{R\; 34} + {R\; 42}} + \frac{V_{5} - V_{3}}{R\; 32}} = 0} & {{Formula}\mspace{14mu} 23} \\{{\frac{V_{4} - V_{0}}{R\; 44} + \frac{V_{4} - V_{1}}{{R\; 13} + {R\; 41}} + \frac{V_{3} - V_{4}}{{R\; 34} + {R\; 42}}} = 0} & {{Formula}\mspace{14mu} 24} \\{{\frac{V_{5} - V_{2}}{R\; 22} + \frac{V_{5} - V_{3}}{R\; 32} + I_{5}} = 0} & {{Formula}\mspace{14mu} 25}\end{matrix}$

Also, because the current that enters n0 and the current that exits fromn5 are equal, below formula 26 is satisfied.I ₀ +I ₅=0  Formula 26

The seven formulas 20 through 26 can be expressed in matrix form. It ispossible to obtain the values of V5, V0, and I₀ by simplifying each rowof that determinant, using the Gauss-Jordan method, for example. It ispossible to calculate a combined resistance λeq,x between n0 and n5 bysubstituting these values into formula 27.

$\begin{matrix}{{\lambda\;{eq}},{x = {\frac{V_{5} - V_{0}}{I} \cdot \frac{lx}{lylz}}}} & {{Formula}\mspace{14mu} 27}\end{matrix}$In formula 27, lx, ly, and lz are the sizes in the x, y, and zdirections of the region in which the small regions 601, 602, 603, and604 are combined, and I is I₀ or I₅.

The equivalent thermal resistance in the Y axis direction of the regionin which the small regions 601, 602, 603, and 604 are combined can beconsidered as the thermal resistance between n6 and n7, and this alsocan be calculated in the same manner.

In FIG. 18, a method was described that obtains an equivalent thermalresistance for a region in which the adjacent small regions 601, 602,603, and 604 are combined in the direction of the XY plane. Because thisis also the same when considering a region in which adjacent regions arecombined in a three-dimensional space, that explanation is omitted.

Also, the calculation method of an equivalent material constant for aregion in which adjacent regions are combined is not limited to theabove method using Kirchoff's law. For example, it is possible to use afinite element method, a calculus of finite differences, or the like.

Modified Example of a Combined Region Equivalent Material ConstantCalculation Method

Here, an example of a method that calculates an equivalent materialconstant for the region in which adjacent regions are combined using afinite element method will be explained. In the example of the method ofsolving with a finite element method, the material constant of the smallregion is deemed to be a spring constant, and a force that works in theregion in which the small regions are combined is obtained.

FIG. 19 is, for example, a plan view viewing three adjacent smallregions 701, 702, and 703 from the direction of the Z axis. The materialconstants possessed by the small regions 701, 702, and 703 are deemed tobe X axis direction spring constants k1, k2, and k3, respectively. Usingthese spring constants in the X axis direction, by creating a stiffnessequation and obtaining a solution with a matrix calculation, it ispossible to obtain a combined equivalent material constant for the Xaxis direction.

Following is an explanation of an example of a method of creating astiffness equation. In FIG. 19, external force that works at a node B0is made p0, and external force that works at a node B3 is made, p3.Displacement at nodes B0, B1, B2, and B3 is made u₀, u₁, u₂, and u₃. Theequilibrium of force at node B0 is expressed by the below equations.k ₁(u ₀ −u ₁)=p0  (Equation 1)In the same manner, the equilibrium at nodes B1, B2, and B3 is asfollows:−k ₁(u ₀ −u ₁)+k ₂(u ₁ −u ₂)=0  (Equation 2)−k ₂(u ₁ −u ₂)+k ₃(u ₂ −u ₃)=0  (Equation 3)−k ₃(u ₂ −u ₃)=p3  (Equation 4)Expressed as a matrix, above equation 1 to 4 become below formula 28.

$\begin{matrix}{\begin{Bmatrix}{p\; 0} \\0 \\0 \\{p\; 3}\end{Bmatrix} = {\begin{bmatrix}k_{1} & {- k_{1}} & 0 & 0 \\{- k_{1}} & {k_{1} + k_{2}} & {- k_{2}} & 0 \\0 & {- k_{2}} & {k_{2} + k_{3}} & {- k_{3}} \\0 & 0 & {- k_{3}} & k_{3}\end{bmatrix}\begin{Bmatrix}u_{0} \\u_{1} \\u_{2} \\u_{3}\end{Bmatrix}}} & {{Formula}\mspace{14mu} 28}\end{matrix}$

In above formula 28, output p3 is calculated from input of a suitable p0and boundary condition (for example, u₀=0). From this p0 and p3, anequivalent spring constant is obtained for the region in which smallregions 701, 702, and 703 are combined.

The above is a modified example of a combined region equivalent materialconstant calculation method. In FIG. 18 a case was explained in whichthe four small regions 601, 602, 603, and 604 are combined, but becausethis is the same if the combined region is constituted by a largernumber of small regions 102, an explanation of such a case is omitted.

Also, in the present embodiment, an explanation was given with theequivalent thermal resistance as a material constant, but it is alsopossible to calculate the equivalent thermal conductivity by obtainingthe reciprocal of the equivalent thermal resistance.

Also, in the present embodiment, an equivalent material constant isobtained for the region in which the divided small regions 102 arecombined in the Z axis direction, and an equivalent material constant isobtained for a region in which these regions combined in the Z axisdirection are further combined in the direction of the XY plane. Theorder of combination is not limited to this; for example, the smallregions 102 may be combined in the Z axis direction after they arecombined in the direction of the XY plane. The small regions 102 may becombined only in the Z axis direction, or only in the direction of theXY plane.

Also, when dividing the structure, it is not necessarily required todivide into each layer in the Z axis direction. For example, it ispossible to divide into regions that reach into a three-dimensionalspace, in the manner of a cube, a rectangular solid, or the like. In therespective divided small regions, it is possible to perform theprocessing that calculates an equivalent material constant for eachsmall region as disclosed in Embodiments 1 and 2, and obtain anequivalent material constant for a region in which adjacent smallregions are combined by the method stated above.

Also, in the present embodiment, by way of example all of the materialsthat constitute the wire pattern portion 103 are the same, and it isassumed that the thermal conductivity is also the same, but the wirepattern portions 103 also may be constituted from a plurality ofmaterials with different thermal conductivity. This is also true for thenon-wire portion 104.

Embodiment 5

FIG. 20 is a functional block diagram that shows an example of theconfiguration of an equivalent material constant calculation system 100in the present embodiment. As shown in FIG. 20, the equivalent materialconstant calculation system 100 is configured from a storage portion 2,a shape data input portion 3, a material data input portion 4, a regionsetting portion 17, a dividing portion 5, a representative materialdetermining portion 18, a material constant selection portion 19, and acombining portion 7.

The equivalent material constant calculation system 100 can beconstructed on, for example, general purpose equipment such as apersonal computer or a workstation (hereinafter, referred to as ‘PC orthe like’). The function of the shape data input portion 3, the materialdata input portion 4, the region setting portion 17, the dividingportion 5, the representative material determining portion 18, thematerial constant selection portion 19, and the combining portion 7 canbe realized by the CPU of a PC or the like executing a predeterminedprogram. The storage portion 2 can employ, other than a storage mediumbuilt into a PC or the like such as a hard disk or RAM, a portablestorage medium such as a flexible disk or memory card, a storage mediumin a storage device on a network, or the like.

The equivalent material constant calculation system 100 can beconstructed by, for example, installing the program that allows acomputer to execute the processing that is performed by the shape datainput portion 3, the material data input portion 4, the region settingportion 17, the dividing portion 5, the representative materialdetermining portion 18, the material constant selection portion 19, andthe combining portion 7 from a storage medium such as a CD-ROM, or bydownload via a communications line, to a desired PC or the like.

The hardware configuration is not limited to the configuration shown inFIG. 20. For example, the function of the equivalent material constantcalculation system 100 may be distributed to a plurality of PCs or thelike that have been connected by an internet or a LAN such thatcommunication is possible, for example.

The shape data input portion 3 inputs shape data of a structure forwhich an equivalent material constant will be calculated, and saves thatdata in the storage portion 2.

The shape data, for example, is shape data that expresses the shape ofeach material that constitutes the structure. An electronic circuitboard can be given as an example of the structure. Ordinarily, shapedata of an electronic circuit board often is created with a CAD system12 for electronic circuit board design and saved in the CAD system 12.The shape data input portion 3 reads information stored in a shapedatabase 9 of the CAD system 12 to the equivalent material constantcalculation system 100.

Also, the input processing of the shape data input portion 3 is notlimited to the case of reading shape data from the shape database 9. Forexample, it may read a file in which the shape data has been stored andinput new data. Alternatively, the shape data input portion 3 mayreceive input of shape data from a designer via an input device such asa keyboard or a mouse provided in a PC or the like.

The material data input portion 4 inputs material constant data thatexpresses the material constants of the materials that constitute thestructure. An example of data that expresses a material constant, if thestructure is an electronic circuit board, is the material constant (forexample, a thermal conductivity) of a material that constitutes theelectronic circuit board. Material constant data of the electroniccircuit board can be read by the material data input portion 4 when thatinformation is saved in a material database 11 in the CAD system 12 forelectronic circuit board design. Also, the possibility of input via afile, keyboard, mouse, or the like is the same as for the shape datainput portion 3.

The region setting portion 17 sets a region in which an equivalentmaterial constant for the structure will be obtained. The region inwhich an equivalent material constant will be obtained can be made apart of the structure or the entire structure. The region settingportion 17, for example, may receive input of data that indicates theregion in which an equivalent material constant will be obtained from adesigner via an input device such as a keyboard or a mouse provided in aPC or the like. Thereby, the designer can designate a region within thestructure in which an equivalent material constant is desired to beobtained.

The dividing portion 5 divides the structure expressed by the shape datastored in the storage portion 2 into a plurality of small regions. Thedividing portion 5 divides the region set by the region setting portion17 into a plurality of small regions. The representative materialdetermining portion 18 determines a material that represents the dividedsmall regions. The material constant selection portion 19 selects thematerial constant of the material that represents the small regiondetermined by the representative material determining portion 18 fromthe material constants input by the material data input portion 2.

The combined portion 7 includes a lamination direction combining portion71 and a perpendicular direction combining portion 72. The laminationdirection combining portion 71 combines, from among the small regionsdivided by the dividing portion 5, a plurality of adjacent small regionsin the lamination direction, and obtains an equivalent materialconstant. The perpendicular direction combining portion 72 combines aplurality of adjacent small regions in the direction perpendicular tothe lamination direction, and obtains an equivalent material constant.Here, the order in which the lamination direction combining portion 71and the perpendicular direction combining portion 72 are allowed tooperate may begin with either the lamination direction combining portion71 or the perpendicular direction combining portion 72. Also only thelamination direction combining portion 71 may be allowed to operate, oronly the perpendicular direction combining portion 72 may be allowed tooperate.

The equivalent material constants obtained in this manner are saved inthe storage portion 2 along with the position and dimensions of thecombined small regions. Data related to the equivalent materialconstants saved in the storage portion 2 is delivered to an analysissystem 13 as necessary. In the analysis system 13, analysis of the flowof heat, stress distribution, electromagnetic fields, hydrokinetics, andthe like of the structure are performed using the delivered data.

FIG. 21 is a flowchart that shows the operation of the equivalentmaterial constant calculation system 100. FIG. 4 shows an example of theshape of a wire layer included in an electronic circuit board that isthe target of an equivalent thermal conductivity calculation.

Following is a description of the flow of operation of the equivalentmaterial constant calculation system 100, with reference to FIG. 20,FIG. 21, and FIG. 4. Here, as one example, processing is described thatcalculates an equivalent thermal conductivity of an electronic circuitboard.

First, the shape data input portion 3 inputs shape data of the electriccircuit board that will be the target of the equivalent thermalconductivity calculation (Step S71). The shape data of the electriccircuit board is created with the CAD system 12, for example. Theelectric circuit board ordinarily is configured by alternately layeringwire layers and insulation layers.

FIG. 4 is a plan view of a plane perpendicular to the laminationdirection of the electronic circuit board, i.e., a wire layer in the XYplane. The wire layer of an electronic circuit board 101 is configuredfrom a wire pattern portion 103 and a non-wire portion 104. Ordinarilythe wire pattern portion 103 is constituted by material with acomparatively high thermal conductivity such as metal material, and thenon-wire portion 104 is often constituted by material with acomparatively low thermal conductivity such as glass, resin, ceramics,or composites of these.

The material data input portion 4 inputs material constant data of thematerials that constitute the electronic circuit board 101 (Step S72).As material constant data, for example, the thermal conductivity(λtrace) of the wire material, which is metal material that constitutesthe wire pattern portion 103 of the electronic circuit board 101, andthe thermal conductivity (λinsulator) of the insulator material, whichis resin material that constitutes the non-wire portion 104, are input.

The region setting portion 17 sets a region for which an equivalentmaterial will be calculated, which is a region included in theelectronic circuit board 101 (Step S73). The region for which anequivalent material will be calculated is designated by input from adesigner, for example. In the present embodiment, a case is described inwhich the entire electronic circuit board 101 is set as the region forwhich an equivalent material will be calculated.

The region set by the region setting portion 17 is not limited to thecase in which the region is the entire electronic circuit board 101; aregion that is a portion of the electronic circuit board 101 also may beset. For example, it is possible to remove a region where it is notnecessary to obtain an equivalent material constant, such as an edgeportion of the electronic circuit board 101 where there are few wirepatterns, from the set region. It is possible to omit the processing bythe dividing portion 5, the representative material determining portion18, the material constant selection portion 19, and the combiningportion 7 for the region removed from the set region. By doing so, thecalculation load for the equivalent material constant calculation islightened.

Because the shapes of the wire pattern portion 103 and the non-wireportion 104 that constitute the electronic circuit board 101 areextremely complicated, in order to make the subsequent processingsimple, the dividing portion 5 divides the electronic circuit board 101into a plurality of small regions (Step S74).

The dividing portion 5, for example, divides the electronic circuitboard 101 into layers of each wire layer or insulation layer in the Zaxis direction. Further, the dividing portion 5 perpendicularly divideseach layer in a respective first axis and second axis of Cartesiancoordinates set as desired. That is, the dividing portion 5 divides eachdivided layer in the XY plane. The small region 102 is one of thedivided small regions.

Division in the direction of the Z axis can performed for each of thewire layers and insulation layers that constitute the electronic circuitboard 101. Division in the direction of the XY plane, for example, asshown in FIG. 4, can divide a layer into 11 equal divisions in thedirection of the X axis and 10 equal divisions in the direction of the Yaxis, dividing the whole into 110 small regions. It is not necessary forthe division into small regions to divide in equal parts in eachdirection. It is also possible to divide into small regions withdifferent sizes as necessary.

It does not matter if this division into the small regions is the samefor each wire layer and insulation layer, or if it is different.

The fineness of the division into small regions can be set as necessary.For example, it is possible to divide the small regions 102 shown inFIG. 4 more finely, and it is also possible to divide a size equal tofour of the small regions 102 as one small region.

Here, when setting the dividing width to be less than the smallest wirewidth of each layer, accuracy further increases. FIG. 22 shows anexample of a case in which the small regions 102 are more finelydivided, and the dividing width is made not more than the wire width.The example shown in FIG. 22 is an example of a case in which the smallregions 102 in FIG. 4 have been further divided. A small region 102 a isone of the divided small regions. The dividing width of the small region102 a is smaller than a wire width h.

Next, referring to FIG. 21, the representative material determiningportion 18 determines the material that represents the respective smallregions (Step S75). The representative material determining portion 18,for example, can make a material that is positioned in the center of asmall region the representative material of that small region. Therepresentative material determining portion 18 also may decide that amaterial in a defined location in the small region is the representativematerial; it is not limited to material located in the center of thesmall region. For example, when the shape in the XY plane of the smallregion is a square, it is possible to make a material that is located atone of the vertexes of this square the representative material.

FIG. 16 shows an example of a small region. The small region 102 shownin FIG. 16 is constituted from a round wire pattern portion 203 thatoccupies about ¼ of the area of the entire small region 102, a wirepattern portion 203 that is a thin lead line drawn out from the roundportion, and a non-wire portion 204, which is the remaining portion ofthe small region 102. In the small region 102, the material located inthe center is the material of the wire pattern portion 203, and so thematerial that represents this small region is determined to be thematerial of the wire pattern.

Next, the material constant selection portion 19 selects the materialconstant of the material that represents the respective small regions(Step S76), based on the material constant that that was input in thematerial constant data input step (Step S72). The material constantselection portion 19 selects the material constant of the representativematerial determined in Step S75 by referring to the material constantdata input in Step S72. The representative material of the small region102 shown in FIG. 16 is the material of the wire pattern. Accordingly,for example, the thermal conductivity of the wire material included inthe material constant data is selected as the representative materialconstant of the small region 102.

The representative material determining portion 18 and the materialconstant selection portion 19 repeat the processing of Step S75 and StepS76 for all of the small regions.

When a representative material constant is obtained for each smallregion, the combining portion 7 obtains an equivalent material constantfor the region in which a plurality of small regions are combined, basedon the representative material constants of each small region (StepS77). The combining portion 7, for example, obtains an equivalentmaterial constant for the region in which a plurality of small regionsadjacent in the X axis direction, Y axis direction, or Z axis directionare combined for at least one direction.

The processing in which the combining portion 7 obtains an equivalentmaterial constant for the region in which a plurality of adjacent smallregions are combined is the same as the processing described using FIG.17 and FIG. 18 in the above embodiment, so that description will beomitted here.

With the processing described using FIG. 17 and FIG. 18 in the aboveembodiment, by obtaining an equivalent material constant for the regionin which a plurality of small regions are combined, it is possible tocalculate an equivalent material constant for each of a plurality ofmedium regions included in the electronic circuit board 101, which areregions that are a portion of the electronic circuit board 101. FIG. 23shows an example of a medium region included in the electronic circuitboard 101. In FIG. 23, a region in the XY plane that has the size offour small regions is made one medium region. A medium region 106 is oneof the medium regions.

In FIG. 23, four small regions are made one medium region, but it ispreferable to change the size of the medium region as necessary. It isalso possible to combine all of the small regions, and obtain oneequivalent material constant for the entire electrical circuit board101.

Also, for example, it is possible to omit the combining processing bythe combining portion 7 for regions in which it is not necessary toobtain an equivalent material constant, such as the edge portions of theelectronic circuit board 101 where there is not much wire pattern. Bydoing so, the calculation load for the equivalent material constantcalculation is reduced.

In the present embodiment, by way of example it is assumed that all ofthe materials that constitute the wire pattern portion 103 are the same,and the thermal conductivities are also the same, but the wire patternportion 103 also may be constituted from a plurality of materials withdiffering thermal conductivity. This is also true for the non-wireportion 104.

Also, in the present embodiment, a case was explained in which anequivalent thermal conductivity of the electronic circuit board isobtained. The equivalent material constant calculation system accordingto the present invention is not limited to an equivalent thermalconductivity calculation system of an electronic circuit board; it alsomay be used in a system that calculates an equivalent material constantof a structure that includes other composite materials. For example, itcan be used in the calculation of an equivalent material constant of asemiconductor component that has a structure in which a semiconductor isprovided in resin, a substrate that includes resin and glass, a sealantresin that includes resin and silica, a conductive adhesive thatincludes resin and silver, or the like.

Also, the equivalent material constant calculation according to thepresent invention is not limited to a system that calculates anequivalent thermal conductivity. For example, an equivalent materialconstant calculation system that calculates an equivalent electricalconductivity, equivalent dielectric constant, equivalent magneticpermeability, equivalent Young's modulus, or other material constants ofcomposite materials is also included in the present invention.

Embodiment 6

Embodiment 6 is a design system that includes the equivalent materialconstant calculation system 100 of Embodiment 1-5. The design systemaccording to the present embodiment is a system for designing astructure constituted from a plurality of materials.

FIG. 24 is a functional block diagram that shows an example of theconfiguration of a design system 15 according to the present embodiment.In the block diagram shown in FIG. 24, the same blocks as in the blockdiagram shown in FIG. 20 are given the same numerals, and thatexplanation is not repeated. Also, because the processing of theequivalent material constant calculation system 100 is the same as inEmbodiment 5, that explanation is also omitted.

The design system 15 includes, in addition to the equivalent materialconstant calculation system 100, a CAD system 12, an analysis system 13,and a design modification portion 14.

The CAD system 12 designs a structure constituted from a plurality ofmaterials, and stores that design data. Shape data and material constantdata is included in the design data. The shape data is saved in a shapedatabase 9, and the material constant data is saved in a materialdatabase 11.

The CAD system 12 is connected such that data communication with a CAM(Computer Aided Manufacturing) system 16 is possible. The CAD system 12sends design data to the CAM system 16.

The CAM system 16 automatically manufactures a structure based on thedesign data received from the CAD system 12. The CAM system 16 is anautomatic manufacturing system invoking a computer. In the CAM system16, a computer transmits a work command to an automatic machine formanufacturing a structure (not shown in the figures).

The analysis system 13 includes an analysis portion 13 a and an outputportion 13 b. The analysis portion 13 a analyzes the flow of heat,pressure distribution, magnetic fields, or hydrokinetics in a structureby simulation, based on the equivalent material constant of thestructure calculated by the equivalent material constant calculationsystem 100 and the design data created by the CAD system 12. The outputportion 13 b outputs the analysis results of the analysis portion 13 a.The output portion 13 b includes a function to send the analysis resultsto the design modification portion 14, and a function to print ordisplay the analysis results such that they are understood by thedesigner. The function to print or display the analysis results isrealized, for example, by a display or printer.

The design modification portion 14 modifies the design data saved in theCAD system 12, based on the analysis results received from the outputportion 13 b of the analysis system 13. Also, the design modificationportion 14 includes a user interface for receiving a design datamodification command from the designer. The design modification portion14 modifies the design data saved in the CAD system 12, based on thedesign data modification command received from the designer.

Following is a description of the method for designing and manufacturinga structure using the design system 15. FIG. 25 is a flowchart thatshows the flow of processing in which the design system 15 manufacturesa structure.

First, the CAD system 12 designs the structure (Step S81). For example,it creates design data with a plurality of different patterns for thesame kind of structure. Shape data and material constant data areincluded in the design data created by the CAD system 12. Those aresaved in the shape database 9 and the material database 11 of the CADsystem 12.

Based on the plurality of design data created in Step S81, theequivalent material constant calculation system 100 calculates anequivalent material constant of the structure expressed by therespective design data (Step S82). The calculation method of theequivalent material constant is the same as the processing in Embodiment5, and therefore is omitted here.

Based on the design data created in Step S81 and the equivalent materialconstant calculated in Step S82, the analysis portion 13 a analyzes theflow of heat, pressure distribution, magnetic fields, or hydrokineticsin the structure expressed by the design data by simulation (Step S83).It is possible to use commercially available CAE (Computer AidedEngineering) software for the analysis processing. Using the analysisportion 13 a, it is possible to investigate whether designspecifications such as temperature, strength, and noise level of thestructure are satisfied, or whether the permissible temperature andstrength of the material of the structure are exceeded. The analysisprocessing by the analysis portion 13 a is performed for each structurethat the plurality of design data expresses.

The output portion 13 b displays the analysis results so that they maybe understood by the designer. Examples of analysis results for the flowof heat in the structure include a heat contour diagram on the surfaceor in a cross section of the structure, a graph in which position isplotted on the horizontal axis and temperature is plotted on thevertical axis, a temperature value at a predetermined position in thestructure, or the like.

Also, the output portion 13 b sends all or a part of the analysisresults to the design modification portion 14. For example, the outputportion 13 b sends data that expresses the temperature in a specifiedportion of the structure, or the like, to the design modificationportion 14 as analysis results.

Based on the analysis results of Step S83, the design modificationportion 14 selects optimum design data from among the plurality ofdesign data (Step S84). For example, the design modification portion 14,when the temperature distribution of the structure has been obtained asanalysis results, selects design data for which the temperature at aparticular portion of the structure does not exceed a certain value asthe design data of the structure that is to be sent to the CAM system16. Design data also can be selected that is judged to have passed notonly heat analysis, but all of the analysis such as stress analysis,magnetic field analysis, and the like. Here, the selected design data isnot necessarily one design data. The design modification portion 14selects design data based on the analysis results, and so it is alsopossible to select design data that is not expected to generate defectseven when manufactured by the CAM system 16.

The design modification portion 14 also can automatically modify thedesign data saved in the CAD system 12 based on the analysis resultsreceived from the output portion 13 b.

The design modification portion 14 also may modify design data saved onthe CAD system 12 based on a design data modification command from thedesigner. The designer can view the analysis results displayed by theoutput portion 13 b and input a design modification command to thedesign modification portion 14.

Design data of a higher quality structure can be obtained due to thedesign data being modified by the design modification portion 14.

With the design modification portion 14, it is possible to perform theanalysis processing of Steps S82 and S83 again for the modified orselected design data. By repeating the selection or modification ofdesign data (Step S84) and the processing of Steps S82 and S83, designdata of a high quality structure can be obtained.

The CAD system 12 sends the ultimately selected design data to the CAMsystem 16. The CAM system 16 creates a mask pattern for manufacturingthe structure based on the design data sent from the CAD system 12 (StepS85). For example, a computer of the CAM system 16 reads the shape dataincluded in the design data and creates a mask pattern having the shapethat the shape data indicates.

The present invention may be embodied in other forms without departingfrom the spirit or essential characteristics thereof. The embodimentsdisclosed in this application are to be considered in all respects asillustrative and not limiting. The scope of the invention is indicatedby the appended claims rather than by the foregoing description, and allchanges which come within the meaning and range of equivalency of theclaims are intended to be embraced therein.

The present invention can be used as an equivalent material constantcalculation system in which it is possible to calculate an equivalentmaterial constant that takes into consideration the directionality ofeach electronic material that constitutes a structure, an equivalentmaterial constant calculation program, an equivalent material constantcalculation method, and a design system and manufacturing method of astructure for which those are used.

1. An equivalent material constant calculation system that calculates an equivalent material constant of a structure constituted by a plurality of materials, comprising: a shape data input portion that inputs shape data that expresses the shape of each material constituting the structure, a material data input portion that inputs material constant data that expresses a material constant of at least one of the materials constituting the structure, a dividing portion that divides the structure into a plurality of small regions, and a small region interior calculation portion that calculates equivalent material constants in the small regions, wherein the small region interior calculation portion expresses, based on the shape data and material constant data, an equivalent material constant for a region that is part of a small region with a function that includes a value in a variable that expresses a position in at least one direction in the small regions, and calculates equivalent material constants in the small region with respect to the at least one direction using the function, and wherein the small region interior calculation portion comprises: a boundary function generating portion that sets a coordinate in the direction of one coordinate axis to u in an orthogonal coordinate system that has been set for the structure and generates, based on the shape data, a boundary function F(u) that expresses a boundary between the materials in a small region, a section setting portion that sets one or more sections for u in the small region according to a domain of the boundary function F(u), a section interior calculation portion that creates, in the section, based on the function F(u) and the material constant data, a function that expresses a position where the material constant is applied, and obtains an equivalent material constant of the coordinate axis direction in the section by integrating the function in the section, and an equivalent material constant generating portion that, based on a section equivalent material constant of each section obtained by the section interior calculation portion, obtains an equivalent material constant of the coordinate axis direction in the small region.
 2. The equivalent material constant calculation system according to claim 1, further comprising a combining portion that obtains, based on the equivalent material constant for the small region, an equivalent material constant for a region in which a plurality of small regions that are adjacent are combined.
 3. The equivalent material constant calculation system according to claim 2, wherein the combining portion obtains the equivalent material constant for a region in which a plurality of the small regions that are adjacent are combined, by deeming the equivalent material constant for each of the plurality of small regions to be a mutually connected resistance, and obtaining a combined resistance.
 4. A design system that includes the equivalent material constant calculation system according to claim 1, comprising: a storage portion that stores design data of the structure including the shape data and the material constant data, an analysis portion that analyzes and outputs the flow of heat, stress distribution, electromagnetic fields, or hydrokinetics of the structure, by simulation based on the equivalent material constant of the structure calculated by the equivalent material constant calculation system and the design data, and a design modification portion that modifies the design data of the storage portion based on a command to modify the design data from a designer.
 5. An equivalent material constant calculation system that calculates an equivalent material constant of a structure constituted by a plurality of materials, comprising: a shape data input portion that inputs shape data that expresses the shape of each material constituting the structure, a material data input portion that inputs material constant data that expresses a material constant of at least one of the materials constituting the structure, a dividing portion that divides the structure into a plurality of small regions, and a small region interior calculation portion that calculates equivalent material constants in the small regions, wherein the small region interior calculation portion expresses, based on the shape data and material constant data, an equivalent material constant for a region that is part of a small region with a function that includes a value in a variable that expresses a position in at least one direction in the small regions, and calculates equivalent material constants in the small region with respect to the at least one direction using the function, and wherein the small region interior calculation portion comprises: a minimum region material constant generating portion that further divides the small regions into a plurality of minimum regions along one or more directions, and obtains an equivalent material constant for each minimum region based on the shape data and the material constant data, a spectrum calculation portion that obtains a frequency spectrum in each minimum region by performing a Fourier transformation of the distribution of the equivalent material constant of the minimum regions in the small region in one or more directions, and an equivalent material constant generating portion that obtains an equivalent material constant for the small region in the one or more directions, based on the frequency spectrum in each of the minimum regions.
 6. The equivalent material constant calculation system according to claim 5, further comprising a combining portion that obtains, based on the equivalent material constant for the small region, an equivalent material constant for a region in which a plurality of small regions that are adjacent are combined.
 7. A design system that includes the equivalent material constant calculation system according to claim 5, comprising: a storage portion that stores design data of the structure including the shape data and the material constant data, an analysis portion that analyzes and outputs the flow of heat, stress distribution, electromagnetic fields, or hydrokinetics of the structure, by simulation based on the equivalent material constant of the structure calculated by the equivalent material constant calculation system and the design data, and a design modification portion that modifies the design data of the storage portion based on a command to modify the design data from a designer.
 8. A storage medium storing an equivalent material constant calculation program that allows a computer to execute processing that calculates an equivalent material constant of a structure constituted by a plurality of materials, the processing comprising: shape data input Processing that inputs shape data that expresses the shape of each material constituting the structure, material data input processing that inputs material constant data that expresses a material constant of at least one of the materials constituting the structure, dividing processing that divides the structure into a plurality of small regions, and small region interior calculation processing that calculates equivalent material constants in the small regions, wherein the small region interior calculation processing expresses, based on the shape data and material constant data, an equivalent material constant in a region that is a portion of a small region with a function that includes a value in a variable that expresses a position in at least one direction in the small regions, and calculates an equivalent material constant for the small region with respect to the at least one direction using the function, and wherein the small region interior calculation processing includes: boundary function generating processing that sets a coordinate in the direction of one coordinate axis to u in an orthogonal coordinate system that has been set for the structure, and generates, based on the shape data, a boundary function F(u) that expresses a boundary between the materials in a small region, section setting processing that sets one or more sections for u in the small region according to a domain of the boundary function F(u), section interior calculation processing that creates, in the section, based on the function F(u) and the material constant data, a function that expresses a position where the material constant is applied, and obtains an equivalent material constant of the coordinate axis direction in the section by integrating the function in the section, and equivalent material constant generating processing that, based on a section equivalent material constant of each section obtained by the section interior calculation portion, obtains an equivalent material constant of the coordinate axis direction in the small region.
 9. A storage medium storing an equivalent material constant calculation program that allows a computer to execute processing that calculates an equivalent material constant of a structure constituted by a plurality of materials, the processing comprising: shape data input processing that inputs shape data that expresses the shape of each material constituting the structure, material data input processing that inputs material constant data that expresses a material constant of at least one of the materials constituting the structure, dividing processing that divides the structure into a plurality of small regions, and small region interior calculation processing that calculates equivalent material constants in the small regions, wherein the small region interior calculation processing expresses, based on the shape data and material constant data, an equivalent material constant in a region that is a portion of a small region with a function that includes a value in a variable that expresses a position in at least one direction in the small regions, and calculates an equivalent material constant for the small region with respect to the at least one direction using the function, and wherein the small region interior calculation processing includes: minimum region material constant generating processing that further divides a small regions into a plurality of minimum regions along one or more directions, and obtains an equivalent material constant for each minimum region based on the shape data and the material constant data, spectrum calculation processing that obtains a frequency spectrum in each minimum region by performing a Fourier transformation of the distribution of the equivalent material constant of the minimum regions in the small region in one or two or more directions, and equivalent material constant generating processing that obtains an equivalent material constant for the small region in the one or more directions, based on the frequency spectrum in each of the minimum regions.
 10. An equivalent material constant calculation method that calculates an equivalent material constant of a structure constituted by a plurality of materials using a computer comprising, a shape data input step in which a shape data input portion provided by the computer inputs shape data that expresses the shape of each material constituting the structure, a material data input step in which a material data input portion provided by the computer inputs material constant data that expresses a material constant of at least one of the materials constituting the structure, a dividing step in which a dividing portion provided by the computer divides the structure into a plurality of small regions, and a small region interior calculation step in which a small region interior calculation portion provided by the computer calculates equivalent material constants in the small regions, wherein the small region interior calculation step, in which a small region interior calculation portion expresses, based on the shape data and material constant data, an equivalent material constant for a region that is a portion of a small region with a function that includes value in a variable a that expresses a location in the small region in at least one direction and calculates an equivalent material constant for the small region with respect to the at least one direction using the function, and wherein the small region interior calculation step comprises: a boundary function generating step of setting a coordinate in the direction of one coordinate axis to u in an orthogonal coordinate system that has been set for the structure, and generating, based on the shape data, a boundary function F(u) that expresses a boundary between the materials within the small region, a section setting step of setting one or more sections for u in the small region according to a domain of the boundary function F(u), a section interior calculation step of creating a function, in the section, that expresses a position where the material constant is applied, based on the function F(u) and the material constant data, and obtaining an equivalent material constant of the coordinate axis direction in the section by integrating the function in the section, and an equivalent material constant generating step of obtaining an equivalent material constant of the coordinate axis direction in the small region, based on a section equivalent material constant of each section which is obtained in the section interior calculation step.
 11. A structure manufacturing method that, using a computer that can access a storage device in which a plurality of design data of a structure constituted by a plurality of materials is stored, manufactures the structure, comprising: a calculating step in which the computer calculates an equivalent material constant of the structure by the equivalent material constant calculation method according to claim 10, an analysis step in which an analysis portion provided by the computer analyzes the flow of heat, stress distribution, electromagnetic field, or hydrokinetics of the structure, by simulation based on the equivalent material constant and the design data, a design data selection step in which a design data selection portion provided by the computer selects design data from among the plurality of design data based on the analysis results obtained by the analysis step for a structure expressed by the plurality of design data stored in the storage device, and a manufacturing step in which a CAM, connected such that data communications are possible with the computer, manufactures a structure based on the design data selected by the design data selection step.
 12. An equivalent material constant calculation method that calculates an equivalent material constant of a structure constituted by a plurality of materials using a computer comprising, a shape data input step in which a shape data input portion provided by the computer inputs shape data that expresses the shape of each material constituting the structure, a material data input step in which a material data input portion provided by the computer inputs material constant data that expresses a material constant of at least one of the materials constituting the structure, a dividing step in which a dividing portion provided by the computer divides the structure into a plurality of small regions, and a small region interior calculation step in which a small region interior calculation portion provided by the computer calculates equivalent material constants in the small regions, wherein the small region interior calculation step, in which a small region interior calculation portion expresses, based on the shape data and material constant data, an equivalent material constant for a region that is a portion of a small region with a function that includes value in a variable a that expresses a location in the small region in at least one direction and calculates an equivalent material constant for the small region with respect to the at least one direction using the function, and wherein the small region interior calculation step comprises: a minimum region material constant generating step of further dividing a small regions into a plurality of minimum regions along one or more directions, and obtaining an equivalent material constant for each minimum region, based on the shape data and the material constant data, a spectrum calculation step of obtaining a frequency spectrum in each minimum region by performing a Fourier transformation of the distribution of the equivalent material constant of the minimum regions in the small region in one or more directions, and an equivalent material constant generating step of obtaining an equivalent material constant for the small region in the one or more directions, based on the frequency spectrum in each of the minimum regions.
 13. A structure manufacturing method that, using a computer that can access a storage device in which a plurality of design data of a structure constituted by a plurality of materials is stored, manufactures the structure, comprising: a calculating step in which the computer calculates an equivalent material constant of the structure by the equivalent material constant calculation method according to claim 12, an analysis step in which an analysis portion provided by the computer analyzes the flow of heat, stress distribution, electromagnetic field, or hydrokinetics of the structure, by simulation based on the equivalent material constant and the design data, a design data selection step in which a design data selection portion provided by the computer selects design data from among the plurality of design data based on the analysis results obtained by the analysis step for a structure expressed by the plurality of design data stored in the storage device, and a manufacturing step in which a CAM, connected such that data communications are possible with the computer, manufactures a structure based on the design data selected by the design data selection step.
 14. An equivalent material constant calculation system that calculates an equivalent material constant of a structure constituted by a plurality of materials, comprising: a shape data input portion that inputs shape data that expresses the shape of each material constituting the structure, a material data input portion that inputs material constant data that expresses a material constant of at least one of the materials constituting the structure, a dividing portion that divides the structure into a plurality of small regions, and a small region interior calculation portion that calculates equivalent material constants in the small regions, wherein the small region interior calculation portion calculates an area of each material included in the small region based on the shape data, obtains a slope of a line that expresses a boundary between the materials relative to a predetermined direction, and calculates an equivalent material constant for the small region based on the slope, the area, and the material constant data.
 15. The equivalent material constant calculation system according to claim 14, further comprising a combining portion that obtains an equivalent material constant for a region in which a plurality of small regions that are adjacent arc combined, based on the equivalent material constant for the small region.
 16. The equivalent material constant calculation system according to claim 15, wherein the combining portion obtains the equivalent material constant for a region in which a plurality of the small regions that are adjacent are combined, by deeming the equivalent material constant for each of the plurality of small regions to be a mutually connected resistance, and obtaining a combined resistance.
 17. A design system that includes the equivalent material constant calculation system according to claim 14, comprising: a storage portion that stores design data of the structure including the shape data and the material constant data, an analysis portion that analyzes and outputs the flow of heat, stress distribution, electromagnetic fields, or hydrokinetics of the structure, by simulation based on the equivalent material constant of the structure calculated by the equivalent material constant calculation system and the design data, and a design modification portion that modifies the design data of the storage portion based on a command to modify the design data from a designer.
 18. An equivalent material constant calculation method that calculates an equivalent material constant of a structure constituted by a plurality of materials using a computer, comprising: a shape data input step in which a shape data input portion provided by the computer inputs shape data that expresses the shape of each material constituting the structure, a material data input step in which a material data input portion provided by the computer inputs material constant data that expresses a material constant of at least one of the materials constituting the structure, a dividing step in which a dividing portion provided by the computer divides the structure into a plurality of small regions, and a small region interior calculation step in which a small region interior calculation portion provided by the computer calculates equivalent material constants in the small regions, wherein in the small region interior calculation step, the small region interior calculation portion calculates an area of each material included in the small region based on the shape data, obtains a slope of a line that expresses a boundary between the materials relative to a predetermined direction, and calculates an equivalent material constant for the small region based on the slope, the area, and the material constant data.
 19. A structure manufacturing method that, using a computer that can access a storage device in which a plurality of design data of a structure constituted by a plurality of materials is stored, manufactures the structure, comprising: a calculating step in which the computer calculates an equivalent material constant of the structure by the equivalent material constant calculation method according to claim 18, an analysis step in which an analysis portion provided by the computer analyzes the flow of heat, stress distribution, electromagnetic field, or hydrokinetics of the structure, by simulation based on the equivalent material constant and the design data, a design data selection step in which a design data selection portion provided by the computer selects design data from among the plurality of design data based on the analysis results obtained by the analysis step for a structure expressed by the plurality of design data stored in the storage device, and a manufacturing step in which a CAM, connected such that data communications are possible with the computer, manufactures a structure based on the design data selected by the design data selection portion.
 20. A storage medium storing an equivalent material constant calculation program that allows a computer to execute processing that the processing calculates an equivalent material constant of a structure constituted by a plurality of materials, the processing comprising: a shape data input processing that inputs shape data that expresses the shape of each material constituting the structure, a material data input processing that inputs material constant data that expresses a material constant of at least one of the materials constituting the structure, a dividing processing that divides the structure into a plurality of small regions, and a small region interior calculation processing that calculates equivalent material constants in the small regions, wherein the small region interior calculation processing calculates an area of each material included in the small region based on the shape data, obtains a slope of a line that expresses a boundary between the materials relative to a predetermined direction, and calculates an equivalent material constant for the small region based on the slope, the area, and the material constant data. 